Quiz
MATH METHODS 2 - COORDINATE GEOMETRY AND LINEAR RELATIONS
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Questions in this quiz (49)
1Find 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] )- A5
- B8
2Find 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] )- A-0.7
- B0.85
3Find 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] )- A3
- B3
- C6
- D1 1/2
- E8
- F3 1/2
4The 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] )- A6
- B8.8
5If 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] )- A4
- B4
6If 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] )- A-4
- B-3
7Find 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]- A9
- B-6
8Find the distance between each of the following (correct to two decimal places):
(3, 6) and (−4, 5)
Answer : approx [blank_start]?[blank_end]- A7.07
9Find the distance between each of the following (correct to two decimal places):
(6, 4) and (−7, 4)
Answer : approx [blank_start]?[blank_end]- A13
10Calculate the perimeter of a triangle with vertices (−3, −4), (1, 5) and (7, −2).
Answer : approx [blank_start]?[blank_end]- A29.27
11There 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]- ADN
12Calculate the gradient of the line:
Answer: [blank_start]?[blank_end]
- A4
13Calculate the gradient of the following line:
Answer - [blank_start]?[blank_end]
- A1/4
14Calculate the gradient of the following line:
Answer - [blank_start]?[blank_end]
- A-2
15For 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]- A-8
16For 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]- A-13
17For 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]- A61
18Find the gradient of the straight line that passes through the points with coordinates
(5a, 2a) and (3a, 6a).
Answer - [blank_start]?[blank_end]- A-2
19Find the gradient of the straight line that passes through the points with coordinates
(5a, 2a) and (5b, 2b).
Answer - [blank_start]?[blank_end]- A2/5
20A 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]- A54
21A 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]- A5/6
22Find 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- A45
23Find 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- A135
24Find 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- A135
25Find 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- A45
26Find 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]- A1
27State 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]- A3
- B6
28State 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]- A-1
- B-4
29Find 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]- A3
- B5
30Find 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]- A3
- B-4
31State 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]- A3
- B-6
32State 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]- A1/2
- B-2
33State 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]- A1/3
- B-5/3
34Express 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]- A2
- B-9
35Express 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]- A5/2
- B-2
36Find 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]- A3
- B-11
37Find 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]- A-2
- B9
38Find 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]- A-1/3
- B11/3
39Find 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]- A11/3
- B-61/3
40For 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]- A2
- B2
- C6
41Find 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]- A2
- B4
42Find 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]- A-2
- B8
43Write, 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]- A2
- B6
44Write, 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]- A-5
- B15
45Find 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]- A-3/2
- B3
46Find 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]- A1/2
- B1 1/2
47Find 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]- A-0.5
- B0.25
48Do 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]- Ayes
49For which of the following does the line pass through the origin?
- Ay + x = 1
- By + 2x = 2(x + 1)
- Cx + y = 0
- Dx − y = 1
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- 2A, B, C
- Author
- Jade Buck
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- English
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