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MATH METHODS 2 - COORDINATE GEOMETRY AND LINEAR RELATIONS

Descripción

2A, B, C
Jade Buck
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Jade Buck
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Resumen del Recurso

Pregunta 1

Pregunta
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] )
Respuesta
  • 5
  • 8

Pregunta 2

Pregunta
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] )
Respuesta
  • -0.7
  • 0.85

Pregunta 3

Pregunta
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] )
Respuesta
  • 3
  • 3
  • 6
  • 1 1/2
  • 8
  • 3 1/2

Pregunta 4

Pregunta
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] )
Respuesta
  • 6
  • 8.8

Pregunta 5

Pregunta
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] )
Respuesta
  • 4
  • 4

Pregunta 6

Pregunta
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] )
Respuesta
  • -4
  • -3

Pregunta 7

Pregunta
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]
Respuesta
  • 9
  • -6

Pregunta 8

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

Pregunta 9

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

Pregunta 10

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

Pregunta 11

Pregunta
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]
Respuesta
  • DN

Pregunta 12

Pregunta
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)
Respuesta
  • 4

Pregunta 13

Pregunta
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)
Respuesta
  • 1/4

Pregunta 14

Pregunta
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)
Respuesta
  • -2

Pregunta 15

Pregunta
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]
Respuesta
  • -8

Pregunta 16

Pregunta
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]
Respuesta
  • -13

Pregunta 17

Pregunta
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]
Respuesta
  • 61

Pregunta 18

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

Pregunta 19

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

Pregunta 20

Pregunta
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]
Respuesta
  • 54

Pregunta 21

Pregunta
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]
Respuesta
  • 5/6

Pregunta 22

Pregunta
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
Respuesta
  • 45

Pregunta 23

Pregunta
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
Respuesta
  • 135

Pregunta 24

Pregunta
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
Respuesta
  • 135

Pregunta 25

Pregunta
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
Respuesta
  • 45

Pregunta 26

Pregunta
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]
Respuesta
  • 1

Pregunta 27

Pregunta
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]
Respuesta
  • 3
  • 6

Pregunta 28

Pregunta
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]
Respuesta
  • -1
  • -4

Pregunta 29

Pregunta
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]
Respuesta
  • 3
  • 5

Pregunta 30

Pregunta
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]
Respuesta
  • 3
  • -4

Pregunta 31

Pregunta
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]
Respuesta
  • 3
  • -6

Pregunta 32

Pregunta
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]
Respuesta
  • 1/2
  • -2

Pregunta 33

Pregunta
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]
Respuesta
  • 1/3
  • -5/3

Pregunta 34

Pregunta
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]
Respuesta
  • 2
  • -9

Pregunta 35

Pregunta
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]
Respuesta
  • 5/2
  • -2

Pregunta 36

Pregunta
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]
Respuesta
  • 3
  • -11

Pregunta 37

Pregunta
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]
Respuesta
  • -2
  • 9

Pregunta 38

Pregunta
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]
Respuesta
  • -1/3
  • 11/3

Pregunta 39

Pregunta
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]
Respuesta
  • 11/3
  • -61/3

Pregunta 40

Pregunta
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]
Respuesta
  • 2
  • 2
  • 6

Pregunta 41

Pregunta
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]
Respuesta
  • 2
  • 4

Pregunta 42

Pregunta
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]
Respuesta
  • -2
  • 8

Pregunta 43

Pregunta
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]
Respuesta
  • 2
  • 6

Pregunta 44

Pregunta
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]
Respuesta
  • -5
  • 15

Pregunta 45

Pregunta
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]
Respuesta
  • -3/2
  • 3

Pregunta 46

Pregunta
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]
Respuesta
  • 1/2
  • 1 1/2

Pregunta 47

Pregunta
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]
Respuesta
  • -0.5
  • 0.25

Pregunta 48

Pregunta
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]
Respuesta
  • yes

Pregunta 49

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