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Mathematics for IGCSE & O level - Coordinate Geometry (Section 3)

1
What is the distance between the points (3, -2) and (7, 1)?
Answer
(C)
5
2
Which of the following equations represents a line parallel to y = -3x + 1?
Answer
(C)
y = -3x - 2
3
What does the gradient of a straight line represent?
Answer
(B)
The slope of the line.
4
Which of these statements about a vertical line is true?
Answer
(B)
It has an undefined gradient.
5
The length of a line segment with endpoints (0, 0) and (3, 4) is:
Answer
(C)
5
6
If the equation of line 1 is y= -x+3 and the equation of line 2 is x+y=5, what is true?
Answer
A
C
D
7
What are the coordinates of the midpoint of a line segment with endpoints (2, 4) and (6, 8)?
Answer
(A)
(4, 6)
8
Calculate the distance between points A(1, 2) and B(4, 6).
Answer
(C)
5
9
In the equation y = -3x + 5, what is the slope and y-intercept?
Answer
(B)
Slope: -3, y-intercept: 5
10
Which of the following sets of lines are perpendicular?
Answer
A
C
11
What is the length of the line segment joining (2, 1) and (6, 4)?
Answer
(C)
5
12
If two lines are perpendicular, what is the relationship between their gradients?
Answer
(C)
The product of the gradients is -1.
13
The equation of a line passes through (1,2) and has a gradient of 3. What is the y-intercept?
Answer
(B)
2
14
What is the length of the line segment with endpoints (1, 1) and (4, 5)?
Answer
(C)
5
15
Which statements are true about the line segment connecting points (1, 2) and (4, 6)?
Answer
A
B
D
16
What is the equation of the line that passes through the point (0, -3) and has a slope of 2?
Answer
(B)
y = 2x - 3
17
What are the two key pieces of information needed to determine the equation of a line?
Answer
B
D
18
The equation of a straight line is of the form y = mx + c. What does 'm' represent?
Answer
(C)
The gradient
19
Find the midpoint of the line segment with endpoints (-2, 5) and (4, -1).
Answer
(A)
(1, 2)
20
A line has a slope of -3 and passes through the point (1, 2). What is the equation of the line?
Answer
(B)
y = -3x + 5
21
What is the gradient of the line described by the equation x + 2y = 4?
Answer
(B)
-1/2
22
What type of line does the equation x = 4 represent?
Answer
(B)
A vertical line
23
What is the gradient of a line passing through the points (0, 0) and (2, 4)?
Answer
(B)
2
24
If two lines cross at right angles at the point (3, 3). One passes through (6, 0). What is the equation of the other line?
Answer
(D)
y = x + 3
25
Which of the following lines is parallel to the line 2x + 3y = 6?
Answer
(B)
y = -2/3x + 1
26
What is the distance between the points (1, 1) and (4, 5)?
Answer
(A)
5
27
Which of the following points lies on the line 2x + y = 5?
Answer
(A)
(1, 2)
28
Which of the following is true about the equation 2x - y + 3 = 0?
Answer
(B)
The gradient is 2.
29
Which point lies on the line 2x + y - 3 = 0?
Answer
(A)
(1, 1)
30
Which of the following points lies on the line y = 2x - 1?
Answer
(A)
(0, -1)
31
What is the equation of a line with gradient -1 that passes through the point (3, -2)?
Answer
(A)
y = -x + 1
32
The equation of a straight line is given by 2x + 3y = 6. What is the y-intercept of this line?
Answer
(B)
3
33
In the equation y = 3x - 2, which is the y-intercept?
Answer
(B)
-2
34
If a line has a gradient of -1/2, what is the gradient of a perpendicular line?
Answer
(B)
2
35
If a line has a gradient of 0, what can be said about it?
Answer
(B)
It is a horizontal line.
36
Which of the following statements are true about the line y = (2/3)x - 4?
Answer
A
B
C
37
What is the gradient of a horizontal line?
Answer
(C)
0
38
What is the gradient of a line perpendicular to a line with equation y = -2/5x + 3?
Answer
(C)
5/2
39
What information is provided by the gradient of a straight-line graph?
Answer
A
C
D
40
Which of the following is the gradient of a line that is perpendicular to a line with equation y = 2/3x + 5?
Answer
(D)
-3/2
41
Which statement is true about the lines y = 2x + 1 and y = 2x - 3?
Answer
(C)
They are parallel
42
Which of the following are true statements about the line y = 2x + 3?
Answer
A
B
C
43
Which of the following is the formula for the midpoint of a line segment with endpoints (x1, y1) and (x2, y2)?
Answer
(B)
((x1 + x2)/2, (y1 + y2)/2)
44
If the gradient of a line is 2, what is the gradient of a line perpendicular to it?
Answer
(A)
-1/2
45
What is the gradient of the line that is parallel to the x-axis?
Answer
(C)
0
46
The equation of a line is given by y = -5x + 7. What is the y-intercept?
Answer
(B)
7
47
Which of the following are required to fully define a straight line in a 2D plane?
Answer
A
C
48
If a line segment has endpoints (2, 3) and (6, 6), what is its gradient?
Answer
(A)
3/4
49
What is the midpoint of the line segment with endpoints (3, -1) and (-5, 5)?
Answer
(A)
(-1, 2)
50
What is the gradient of the line segment connecting the points (0, 5) and (3, 5)?
Answer
(A)
0