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Mathematics for IGCSE & O level - Coordinate Geometry (Section 4)

1
What is the gradient of the line which has the equation -x + 3y = 6?
Answer
(B)
1/3
2
What is the length of the line segment between the points (1, 1) and (4, 5)?
Answer
(C)
5
3
What do parallel lines have in common?
Answer
(B)
Same gradients
4
What is the midpoint of the line segment with endpoints (-3, 7) and (5, -1)?
Answer
(A)
(1, 3)
5
Which of the following points does *not* lie on the line 2x - y = 4?
Answer
(D)
(3, 2)
6
What is the midpoint of the line segment with end points (-2, 5) and (4, -1)?
Answer
(A)
(1, 2)
7
Determine the equation of a line that passes through the point (1, 4) and has a gradient of 3.
Answer
(B)
y = 3x - 1
8
The line segment AB has endpoints A(1, 5) and B(3, 9). What is the length of AB?
Answer
(D)
2 * sqrt(5)
9
Which equation represents a horizontal line?
Answer
(B)
y = 3
10
Which of the following is not a form of a straight line equation?
Answer
(D)
y = ax^2 + bx + c
11
What is the y-intercept of the line that passes through the points (1, 2) and (3, 8)?
Answer
(A)
-1
12
Which of the following equations represents a line perpendicular to the line y = (1/4)x + 2 and passing through the point (0, 0)?
Answer
(A)
y = -4x
13
Which of the following equations is in the general form of a straight line?
Answer
A
B
14
Which equation represents a line parallel to y = 4x - 7?
Answer
(B)
y = 4x + 2
15
What is the gradient of the line 3x + 2y = 6?
Answer
(B)
-3/2
16
Find the length of the line segment connecting the points (0, 0) and (3, 4).
Answer
(C)
5
17
Which of the following statements is true regarding the line perpendicular to y = (1/3)x + 2?
Answer
(B)
The gradient is -3
18
A line segment has endpoints A(1, 1) and B(4, 5). Which of the following statements is correct?
Answer
A
B
D
19
What is the equation of a line that is perpendicular to y = x + 3 and passes through the point (1, 2)?
Answer
(C)
y = x + 1
20
Which of the following equations represent parallel lines?
Answer
A
D
21
What is the x-intercept of the line y = 3x + 6?
Answer
(D)
-2
22
Which of the following statements are true about the line 2x + y - 6 = 0?
Answer
A
B
D
23
What is the midpoint of a line segment with endpoints (2, 4) and (6, 8)?
Answer
(A)
(4, 6)
24
Which of the following is equal to the length of the line segment connecting the points A(2, 3) and B(5, 7)?
Answer
(A)
5
25
Which of the following equations, in general form, represents a line with a gradient of -2/3?
Answer
(A)
2x + 3y = 6
26
Which of the following represents the length of a line segment with endpoints (x1, y1) and (x2, y2)?
Answer
A
C
27
The line L passes through the points (0, 4) and (2, 0). What is the gradient of L?
Answer
(D)
-4/2
28
What is the equation of the line that passes through (1, 1) and has a gradient of 2?
Answer
(B)
y = 2x - 1
29
Which of the following statements is true about the line y = -x + 4?
Answer
A
B
D
30
What is the gradient of a line passing through the points (1, 3) and (5, 7)?
Answer
(A)
1/2
31
What information is needed to determine the equation of a straight line?
Answer
(B)
The gradient and a point on the line
32
What is the relationship between the gradients of two perpendicular lines?
Answer
(B)
They multiply to -1.
33
What is the y-intercept of the line 5x - 2y = 10?
Answer
(C)
2
34
The length of a horizontal line segment is 5, and the length of the vertical side is 3. What is the length of the hypotenuse?
Answer
(C)
sqrt(34)
35
What is the formula for the gradient of a line?
Answer
(C)
(y2 - y1) / (x2 - x1)
36
Which of the following statements are true about the equation 4x + 3y = 12?
Answer
A
B
C
37
What is the general form of the equation of a straight line?
Answer
(A)
y = mx + c
38
What are the gradient and y-intercept of the line represented by the equation 4x - 2y = 8?
Answer
(B)
Gradient = -2, y-intercept = 4
39
What is the equation of the line that is parallel to y = 2x - 1 and passes through the point (0, 0)?
Answer
(B)
y = 2x
40
If a line has a gradient of m, what is the gradient of a line perpendicular to it?
Answer
(D)
-1/m
41
What is the length of the line segment joining the points (1, 2) and (4, 6)?
Answer
(A)
5
42
If two lines are perpendicular, what is the product of their gradients?
Answer
(B)
-1
43
Which equation represents a vertical line?
Answer
(A)
x = 5
44
Which of the following are properties of a line with the equation y = -3x + 5?
Answer
A
B
45
A line has an x-intercept of 3 and a y-intercept of -2. What is its gradient?
Answer
(B)
2/3
46
Which of the following equations represents a line passing through (2, 3) and (-1, 0)?
Answer
(A)
y = x + 1
47
Which of the following equations represents a line with a gradient of -3 and a y-intercept of 5?
Answer
(B)
y = -3x + 5
48
Find the midpoint of the line segment joining the points A(-1, 3) and B(5, 7).
Answer
(A)
(2, 5)
49
The equation of a line is 3x - 4y = 12. What is the x-intercept?
Answer
(D)
-4