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MATH METHODS 2 - COORDINATE GEOMETRY AND LINEAR RELATIONS

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2A, B, C
Jade Buck
Quiz by Jade Buck, updated more than 1 year ago
Jade Buck
Created by Jade Buck over 6 years ago
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Resource summary

Question 1

Question
Find the coordinates of M, the midpoint of AB, where A and B have the coordinates: A(2,12), B(8,4) ( [blank_start]x[blank_end] . [blank_start]y[blank_end] )
Answer
  • 5
  • 8

Question 2

Question
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) ( [blank_start]x[blank_end] , [blank_start]y[blank_end] )
Answer
  • -0.7
  • 0.85

Question 3

Question
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 - ( [blank_start]x[blank_end] , [blank_start]y[blank_end] ) AC - ( [blank_start]x[blank_end] , [blank_start]y[blank_end] ) BC - ( [blank_start]x[blank_end] , [blank_start]y[blank_end] )
Answer
  • 3
  • 3
  • 6
  • 1 1/2
  • 8
  • 3 1/2

Question 4

Question
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? ( [blank_start]x[blank_end] , [blank_start]y[blank_end] )
Answer
  • 6
  • 8.8

Question 5

Question
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: ( [blank_start]x[blank_end] , [blank_start]y[blank_end] )
Answer
  • 4
  • 4

Question 6

Question
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: ( [blank_start]x[blank_end] . [blank_start]y[blank_end] )
Answer
  • -4
  • -3

Question 7

Question
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 = [blank_start]?[blank_end] b = [blank_start]?[blank_end]
Answer
  • 9
  • -6

Question 8

Question
Find the distance between each of the following (correct to two decimal places): (3, 6) and (−4, 5) Answer : approx [blank_start]?[blank_end]
Answer
  • 7.07

Question 9

Question
Find the distance between each of the following (correct to two decimal places): (6, 4) and (−7, 4) Answer : approx [blank_start]?[blank_end]
Answer
  • 13

Question 10

Question
Calculate the perimeter of a triangle with vertices (−3, −4), (1, 5) and (7, −2). Answer : approx [blank_start]?[blank_end]
Answer
  • 29.27

Question 11

Question
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 - [blank_start]?[blank_end]
Answer
  • DN

Question 12

Question
Calculate the gradient of the line: Answer: [blank_start]?[blank_end]
Image:
Screen Shot 2018 06 26 At 8.37.39 Pm (binary/octet-stream)
Answer
  • 4

Question 13

Question
Calculate the gradient of the following line: Answer - [blank_start]?[blank_end]
Image:
Screen Shot 2018 06 26 At 8.39.24 Pm (binary/octet-stream)
Answer
  • 1/4

Question 14

Question
Calculate the gradient of the following line: Answer - [blank_start]?[blank_end]
Image:
Screen Shot 2018 06 26 At 8.41.02 Pm (binary/octet-stream)
Answer
  • -2

Question 15

Question
For the following, find the gradient of the line that passes through the two points with the given coordinates: (5, 8), (6, 0) Answer - [blank_start]?[blank_end]
Answer
  • -8

Question 16

Question
For the following, find the gradient of the line that passes through the two points with the given coordinates: (−5, 25), (−8, 64) Answer - [blank_start]?[blank_end]
Answer
  • -13

Question 17

Question
For the following, find the gradient of the line that passes through the two points with the given coordinates: (5, 125), (4, 64) Answer - [blank_start]?[blank_end]
Answer
  • 61

Question 18

Question
Find the gradient of the straight line that passes through the points with coordinates (5a, 2a) and (3a, 6a). Answer - [blank_start]?[blank_end]
Answer
  • -2

Question 19

Question
Find the gradient of the straight line that passes through the points with coordinates (5a, 2a) and (5b, 2b). Answer - [blank_start]?[blank_end]
Answer
  • 2/5

Question 20

Question
A line has gradient 6 and passes through the points with coordinates (−1, 6) and (7, a). Find the value of a. Answer: a = [blank_start]?[blank_end]
Answer
  • 54

Question 21

Question
A line has gradient −6 and passes through the points with coordinates (1, 6) and (b, 7). Find the value of b. Answer: b = [blank_start]?[blank_end]
Answer
  • 5/6

Question 22

Question
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: [blank_start]?[blank_end] degrees
Answer
  • 45

Question 23

Question
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: [blank_start]?[blank_end] degrees
Answer
  • 135

Question 24

Question
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 = [blank_start]?[blank_end] degrees
Answer
  • 135

Question 25

Question
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 = [blank_start]?[blank_end] degrees
Answer
  • 45

Question 26

Question
Find the gradient of a straight line which is inclined at an angle of 45◦ to the positive direction of the x-axis. Answer: [blank_start]?[blank_end]
Answer
  • 1

Question 27

Question
State the gradient and y-axis intercept of the graph of the equation: y = 3x + 6 m = [blank_start]?[blank_end] c = [blank_start]?[blank_end]
Answer
  • 3
  • 6

Question 28

Question
State the gradient and y-axis intercept of the graph of the equation: y = −x − 4 m = [blank_start]?[blank_end] c = [blank_start]?[blank_end]
Answer
  • -1
  • -4

Question 29

Question
Find the equation of the straight line with gradient 3 and y-axis intercept 5. y = [blank_start]m[blank_end]x + [blank_start]c[blank_end]
Answer
  • 3
  • 5

Question 30

Question
Find the equation of the straight line with gradient 3 and y-axis intercept −4. y = [blank_start]m[blank_end]x + [blank_start]c[blank_end]
Answer
  • 3
  • -4

Question 31

Question
State the gradient and y-axis intercept of the graph of the equation: 3x − y = 6 m = [blank_start]?[blank_end] c = [blank_start]?[blank_end]
Answer
  • 3
  • -6

Question 32

Question
State the gradient and y-axis intercept of the graph of the equation: 5x − 10y = 20 m = [blank_start]?[blank_end] c = [blank_start]?[blank_end]
Answer
  • 1/2
  • -2

Question 33

Question
State the gradient and y-axis intercept of the graph of the equation: 2x − 6y = 10 m = [blank_start]?[blank_end] c = [blank_start]?[blank_end]
Answer
  • 1/3
  • -5/3

Question 34

Question
Express in gradient–intercept form and hence state the gradient and y-axis intercept of the following linear relations: 2x − y = 9 m = [blank_start]?[blank_end] c = [blank_start]?[blank_end]
Answer
  • 2
  • -9

Question 35

Question
Express in gradient–intercept form and hence state the gradient and y-axis intercept of the following linear relations: 5x − 2y = 4 m = [blank_start]?[blank_end] c = [blank_start]?[blank_end]
Answer
  • 5/2
  • -2

Question 36

Question
Find the equation of the straight line that has gradient 3 and passes through the point with coordinates (6, 7). y = [blank_start]m[blank_end]x + [blank_start]c[blank_end]
Answer
  • 3
  • -11

Question 37

Question
Find the equation of the straight line that has gradient −2 and passes through the point with coordinates (1, 7). y = [blank_start]m[blank_end]x + [blank_start]c[blank_end]
Answer
  • -2
  • 9

Question 38

Question
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 = [blank_start]m[blank_end]x + [blank_start]c[blank_end]
Answer
  • -1/3
  • 11/3

Question 39

Question
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 = [blank_start]m[blank_end]x + [blank_start]c[blank_end]
Answer
  • 11/3
  • -61/3

Question 40

Question
For the straight line that has y-axis intercept 6 and passes through the point with coordinates (1, 8), find: the gradient = [blank_start]?[blank_end] the equation = y = [blank_start]m[blank_end]x + [blank_start]c[blank_end]
Answer
  • 2
  • 2
  • 6

Question 41

Question
Find the equation of the straight line that passes through the point (1, 6) and has gradient 2. y = [blank_start]m[blank_end]x + [blank_start]c[blank_end]
Answer
  • 2
  • 4

Question 42

Question
Find the equation of the straight line that passes through the point (1, 6) and has gradient -2. y = [blank_start]m[blank_end]x + [blank_start]c[blank_end]
Answer
  • -2
  • 8

Question 43

Question
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 = [blank_start]m[blank_end]x + [blank_start]c[blank_end]
Answer
  • 2
  • 6

Question 44

Question
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 = [blank_start]m[blank_end]x + [blank_start]c[blank_end]
Answer
  • -5
  • 15

Question 45

Question
Find equations defining the lines which pass through the following pairs of points: (2, 0), (0, 3) y = [blank_start]m[blank_end]x + [blank_start]c[blank_end]
Answer
  • -3/2
  • 3

Question 46

Question
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 = [blank_start]m[blank_end]x + [blank_start]c[blank_end]
Answer
  • 1/2
  • 1 1/2

Question 47

Question
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 = [blank_start]m[blank_end]x + [blank_start]c[blank_end]
Answer
  • -0.5
  • 0.25

Question 48

Question
Do the points P(1, −3), Q(2, 1) and R(2 1/2 , 3) lie on the same straight line? Answer - [blank_start]?[blank_end]
Answer
  • yes

Question 49

Question
For which of the following does the line pass through the origin?
Answer
  • y + x = 1
  • y + 2x = 2(x + 1)
  • x + y = 0
  • x − y = 1
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