MATH METHODS 2 - COORDINATE GEOMETRY AND LINEAR RELATIONS

Question 1 of 49

2

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Find the coordinates of M, the midpoint of AB, where A and B have the coordinates:
A(2,12), B(8,4)

( . )

Explanation

Question 2 of 49

2

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Find the coordinates of M, the midpoint of AB, where A and B have the coordinates:
A(3.6, -2.8), B(-5, 4.5)

( , )

Explanation

Question 3 of 49

6

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Find the midpoints of each of the sides of a triangle ABC, where A is (1, 1), B is (5, 5)
and C is (11, 2).

AB - ( , )
AC - ( , )
BC - ( , )

Explanation

Question 4 of 49

2

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The secretary of a motocross club wants to organise two meetings on the same weekend. One is a hill climb starting from point A(3.1, 7.1) and the other is a circuit event with the start at B(8.9, 10.5), as shown on the map. Only one ambulance can be provided. The ambulance can be called up by radio, so it is decided to keep it at C, halfway between A and B.
What are the coordinates of C?

( , )

Explanation

Question 5 of 49

1

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If M is the midpoint of XY, find the coordinates of Y when X and M have the following
coordinates:

X(−4, 2), M(0, 3)

Answer: ( , )

Explanation

Question 6 of 49

1

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If M is the midpoint of XY, find the coordinates of Y when X and M have the following
coordinates:

X(4, −3), M(0, −3)

Answer: ( . )

Explanation

Question 7 of 49

2

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Find the coordinates of the midpoint of the line segment joining (1, 4) and (a, b), in
terms of a and b. If (5, −1) is the midpoint, find the values of a and b.

Answer:

a =
b =

Explanation

Question 8 of 49

1

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Find the distance between each of the following (correct to two decimal places):

(3, 6) and (−4, 5)

Answer : approx

Explanation

Question 9 of 49

1

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Find the distance between each of the following (correct to two decimal places):

(6, 4) and (−7, 4)

Answer : approx

Explanation

Question 10 of 49

1

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Calculate the perimeter of a triangle with vertices (−3, −4), (1, 5) and (7, −2).

Answer : approx

Explanation

Question 11 of 49

1

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There is an off-shore oil drilling platform in Bass Strait situated at D(0, 6), where
1 unit = 5 km. Pipes for this oil drill come ashore at M(−6, 1) and N(3, −1). Assuming
the pipelines are straight, which is the shorter DM or DN?

Answer -

Explanation

Question 12 of 49

1

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Calculate the gradient of the line:

Answer:

Explanation

Question 13 of 49

1

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Calculate the gradient of the following line:

Answer -

Explanation

Question 14 of 49

1

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Calculate the gradient of the following line:

Answer -

Explanation

Question 15 of 49

1

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For the following, find the gradient of the line that passes through the two points with the given coordinates:

(5, 8), (6, 0)

Answer -

Explanation

Question 16 of 49

1

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For the following, find the gradient of the line that passes through the two points with the given coordinates:

(−5, 25), (−8, 64)

Answer -

Explanation

Question 17 of 49

1

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For the following, find the gradient of the line that passes through the two points with the given coordinates:

(5, 125), (4, 64)

Answer -

Explanation

Question 18 of 49

1

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Find the gradient of the straight line that passes through the points with coordinates
(5a, 2a) and (3a, 6a).

Answer -

Explanation

Question 19 of 49

1

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Find the gradient of the straight line that passes through the points with coordinates
(5a, 2a) and (5b, 2b).

Answer -

Explanation

Question 20 of 49

1

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A line has gradient 6 and passes through the points with coordinates (−1, 6) and
(7, a). Find the value of a.

Answer: a =

Explanation

Question 21 of 49

1

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A line has gradient −6 and passes through the points with coordinates (1, 6) and
(b, 7). Find the value of b.

Answer: b =

Explanation

Question 22 of 49

1

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Find the angle, correct to two decimal places, that the lines joining the given points
make with the positive direction of the x-axis:

(0, 3), (−3, 0)

Answer: degrees

Explanation

Question 23 of 49

1

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Find the angle, correct to two decimal places, that the lines joining the given points make with the positive direction of the x-axis:

(c, b), (b, c)

Answer: degrees

Explanation

Question 24 of 49

1

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Find the angle, correct to two decimal places, that the lines joining the given points make with the positive direction of the x-axis:

(0, −5), (−5, 0)

Answer = degrees

Explanation

Question 25 of 49

1

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Find the angle, correct to two decimal places, that the lines joining the given points make with the positive direction of the x-axis:

(−4, −2), (6, 8)

Answer = degrees

Explanation

Question 26 of 49

1

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Find the gradient of a straight line which is inclined at an angle of 45◦ to the positive direction of the x-axis.

Answer:

Explanation

Question 27 of 49

2

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State the gradient and y-axis intercept of the graph of the equation:

y = 3x + 6

m =
c =

Explanation

Question 28 of 49

2

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State the gradient and y-axis intercept of the graph of the equation:

y = −x − 4

m =
c =

Explanation

Question 29 of 49

2

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Find the equation of the straight line with gradient 3 and y-axis intercept 5.

y = x +

Explanation

Question 30 of 49

2

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Find the equation of the straight line with gradient 3 and y-axis intercept −4.

y = x +

Explanation

Question 31 of 49

2

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State the gradient and y-axis intercept of the graph of the equation:

3x − y = 6

m =
c =

Explanation

Question 32 of 49

2

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State the gradient and y-axis intercept of the graph of the equation:

5x − 10y = 20

m =
c =

Explanation

Question 33 of 49

2

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State the gradient and y-axis intercept of the graph of the equation:

2x − 6y = 10

m =
c =

Explanation

Question 34 of 49

2

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Express in gradient–intercept form and hence state the gradient and y-axis intercept of the following linear relations:

2x − y = 9

m =
c =

Explanation

Question 35 of 49

2

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Express in gradient–intercept form and hence state the gradient and y-axis intercept of the following linear relations:

5x − 2y = 4

m =
c =

Explanation

Question 36 of 49

2

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Find the equation of the straight line that has gradient 3 and passes through the point with coordinates (6, 7).

y = x +

Explanation

Question 37 of 49

2

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Find the equation of the straight line that has gradient −2 and passes through the point with coordinates (1, 7).

y = x +

Explanation

Question 38 of 49

2

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Find the equations of the straight lines passing through the following pairs of points.
(Express your answer in gradient–intercept form.)

(−1, 4), (2, 3)

y = x +

Explanation

Question 39 of 49

2

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Find the equations of the straight lines passing through the following pairs of points.
(Express your answer in gradient–intercept form.)

(5, −2), (8, 9)

y = x +

Explanation

Question 40 of 49

3

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For the straight line that has y-axis intercept 6 and passes through the point with coordinates (1, 8), find:

the gradient =

the equation = y = x +

Explanation

Question 41 of 49

2

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Find the equation of the straight line that passes through the point (1, 6) and has
gradient 2.

y = x +

Explanation

Question 42 of 49

2

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Find the equation of the straight line that passes through the point (1, 6) and has
gradient -2.

y = x +

Explanation

Question 43 of 49

2

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Write, in the form y = mx + c, the equations of the lines which have the given gradient
and pass through the given point:

m = 2; (−1, 4)

y = x +

Explanation

Question 44 of 49

2

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Write, in the form y = mx + c, the equations of the lines which have the given gradient
and pass through the given point:

m = −5; (3, 0)

y = x +

Explanation

Question 45 of 49

2

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Find equations defining the lines which pass through the following pairs of points:

(2, 0), (0, 3)

y = x +

Explanation

Question 46 of 49

2

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Find the equations, in the form y = mx + c, of the lines which pass through the
following pairs of points:

(−3, 0), (3, 3)

y = x +

Explanation

Question 47 of 49

2

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Find the equations, in the form y = mx + c, of the lines which pass through the
following pairs of points:

(−3, 1.75), (4.5, −2)

y = x +

Explanation

Question 48 of 49

1

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Do the points P(1, −3), Q(2, 1) and R(2 1/2 , 3) lie on the same straight line?

Answer -

	Created by Jade Buck over 6 years ago

2A, B, C

MATH METHODS 2 - COORDINATE GEOMETRY AND LINEAR RELATIONS

Question 1 of 49

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Find the coordinates of M, the midpoint of AB, where A and B have the coordinates: A(2,12), B(8,4) ( . )

Explanation

Question 2 of 49

Fill the blank spaces to complete the text.

Find the coordinates of M, the midpoint of AB, where A and B have the coordinates: A(3.6, -2.8), B(-5, 4.5) ( , )

Explanation

Question 3 of 49

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Find the midpoints of each of the sides of a triangle ABC, where A is (1, 1), B is (5, 5) and C is (11, 2). AB - ( , ) AC - ( , ) BC - ( , )

Explanation

Question 4 of 49

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Explanation

Question 5 of 49

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If M is the midpoint of XY, find the coordinates of Y when X and M have the following coordinates: X(−4, 2), M(0, 3) Answer: ( , )

Explanation

Question 6 of 49

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If M is the midpoint of XY, find the coordinates of Y when X and M have the following coordinates: X(4, −3), M(0, −3) Answer: ( . )

Explanation

Question 7 of 49

Fill the blank spaces to complete the text.

Find the coordinates of the midpoint of the line segment joining (1, 4) and (a, b), in terms of a and b. If (5, −1) is the midpoint, find the values of a and b. Answer: a = b =

Explanation

Question 8 of 49

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Find the distance between each of the following (correct to two decimal places): (3, 6) and (−4, 5) Answer : approx

Explanation

Question 9 of 49

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Find the distance between each of the following (correct to two decimal places): (6, 4) and (−7, 4) Answer : approx

Explanation

Question 10 of 49

Fill the blank space to complete the text.

Calculate the perimeter of a triangle with vertices (−3, −4), (1, 5) and (7, −2). Answer : approx

Explanation

Question 11 of 49

Fill the blank space to complete the text.

There is an off-shore oil drilling platform in Bass Strait situated at D(0, 6), where 1 unit = 5 km. Pipes for this oil drill come ashore at M(−6, 1) and N(3, −1). Assuming the pipelines are straight, which is the shorter DM or DN? Answer -

Explanation

Question 12 of 49

Fill the blank space to complete the text.

Calculate the gradient of the line: Answer:

Explanation

Question 13 of 49

Fill the blank space to complete the text.

Calculate the gradient of the following line: Answer -

Explanation

Question 14 of 49

Fill the blank space to complete the text.

Calculate the gradient of the following line: Answer -

Explanation

Question 15 of 49

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For the following, find the gradient of the line that passes through the two points with the given coordinates: (5, 8), (6, 0) Answer -

Explanation

Question 16 of 49

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For the following, find the gradient of the line that passes through the two points with the given coordinates: (−5, 25), (−8, 64) Answer -

Explanation

Question 17 of 49

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For the following, find the gradient of the line that passes through the two points with the given coordinates: (5, 125), (4, 64) Answer -

Explanation

Question 18 of 49

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Find the gradient of the straight line that passes through the points with coordinates (5a, 2a) and (3a, 6a). Answer -

Explanation

Question 19 of 49

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Find the gradient of the straight line that passes through the points with coordinates (5a, 2a) and (5b, 2b). Answer -

Explanation

Question 20 of 49

Fill the blank space to complete the text.

A line has gradient 6 and passes through the points with coordinates (−1, 6) and (7, a). Find the value of a. Answer: a =

Find the coordinates of M, the midpoint of AB, where A and B have the coordinates:
A(2,12), B(8,4)

( . )

Find the coordinates of M, the midpoint of AB, where A and B have the coordinates:
A(3.6, -2.8), B(-5, 4.5)

( , )

Find the midpoints of each of the sides of a triangle ABC, where A is (1, 1), B is (5, 5)
and C is (11, 2).

AB - ( , )
AC - ( , )
BC - ( , )

If M is the midpoint of XY, find the coordinates of Y when X and M have the following
coordinates:

X(−4, 2), M(0, 3)

Answer: ( , )

If M is the midpoint of XY, find the coordinates of Y when X and M have the following
coordinates:

X(4, −3), M(0, −3)

Answer: ( . )

Find the coordinates of the midpoint of the line segment joining (1, 4) and (a, b), in
terms of a and b. If (5, −1) is the midpoint, find the values of a and b.

Answer:

a =
b =

Find the distance between each of the following (correct to two decimal places):

(3, 6) and (−4, 5)

Answer : approx

Find the distance between each of the following (correct to two decimal places):

(6, 4) and (−7, 4)

Answer : approx

Calculate the perimeter of a triangle with vertices (−3, −4), (1, 5) and (7, −2).

Answer : approx

There is an off-shore oil drilling platform in Bass Strait situated at D(0, 6), where
1 unit = 5 km. Pipes for this oil drill come ashore at M(−6, 1) and N(3, −1). Assuming
the pipelines are straight, which is the shorter DM or DN?

Answer -

Calculate the gradient of the line:

Answer:

Calculate the gradient of the following line:

Answer -

Calculate the gradient of the following line:

Answer -

For the following, find the gradient of the line that passes through the two points with the given coordinates:

(5, 8), (6, 0)

Answer -

For the following, find the gradient of the line that passes through the two points with the given coordinates:

(−5, 25), (−8, 64)

Answer -

For the following, find the gradient of the line that passes through the two points with the given coordinates:

(5, 125), (4, 64)

Answer -

Find the gradient of the straight line that passes through the points with coordinates
(5a, 2a) and (3a, 6a).

Answer -

Find the gradient of the straight line that passes through the points with coordinates
(5a, 2a) and (5b, 2b).

Answer -

A line has gradient 6 and passes through the points with coordinates (−1, 6) and
(7, a). Find the value of a.

Answer: a =

A line has gradient −6 and passes through the points with coordinates (1, 6) and
(b, 7). Find the value of b.

Answer: b =

Find the angle, correct to two decimal places, that the lines joining the given points
make with the positive direction of the x-axis:

(0, 3), (−3, 0)

Answer: degrees

Find the angle, correct to two decimal places, that the lines joining the given points make with the positive direction of the x-axis:

(c, b), (b, c)

Answer: degrees

Find the angle, correct to two decimal places, that the lines joining the given points make with the positive direction of the x-axis:

(0, −5), (−5, 0)

Answer = degrees

Find the angle, correct to two decimal places, that the lines joining the given points make with the positive direction of the x-axis:

(−4, −2), (6, 8)

Answer = degrees

Find the gradient of a straight line which is inclined at an angle of 45◦ to the positive direction of the x-axis.

Answer:

State the gradient and y-axis intercept of the graph of the equation:

y = 3x + 6

m =
c =

State the gradient and y-axis intercept of the graph of the equation:

y = −x − 4

m =
c =

Find the equation of the straight line with gradient 3 and y-axis intercept 5.

y = x +

Find the equation of the straight line with gradient 3 and y-axis intercept −4.

y = x +

State the gradient and y-axis intercept of the graph of the equation:

3x − y = 6

m =
c =

State the gradient and y-axis intercept of the graph of the equation:

5x − 10y = 20

m =
c =

State the gradient and y-axis intercept of the graph of the equation:

2x − 6y = 10

m =
c =

Express in gradient–intercept form and hence state the gradient and y-axis intercept of the following linear relations:

2x − y = 9

m =
c =

Express in gradient–intercept form and hence state the gradient and y-axis intercept of the following linear relations:

5x − 2y = 4

m =
c =

Find the equation of the straight line that has gradient 3 and passes through the point with coordinates (6, 7).

y = x +

Find the equation of the straight line that has gradient −2 and passes through the point with coordinates (1, 7).

y = x +