MATH METHODS 2 - COORDINATE GEOMETRY AND LINEAR RELATIONS

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 - ( , )

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?

( , )

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 +

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 +

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 +

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 +

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

y = x +

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

y = x +

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 +

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 +

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

(2, 0), (0, 3)

y = x +

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 +

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 +

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

Answer -