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Cambridge IGCSE Maths: Coordinate geometry — Practice Questions & Answers
Coordinate geometry connects algebra and shapes by describing points and lines on the Cartesian plane. This article covers plotting points, finding the gradient between two points, calculating the length and midpoint of a line segment, the straight-line equation $y=mx+c$, reading off gradient and intercept, the rules for parallel and perpendicular gradients, and how to build the equation of a line from given information.
154 practice questions available for this topic — here are 10 with full answers and explanations.
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Practice questions with answers
1
Multiple choice · Easy
In which quadrant does the point $(-3,5)$ lie?
Second quadrant
First quadrant
Third quadrant
Fourth quadrant
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Why A negative $x$ and a positive $y$ place a point in the second quadrant (top left).
2
Multiple choice · Easy
What is the midpoint of the line segment joining $(2,4)$ and $(6,8)$?
$(4,6)$
$(8,12)$
$(4,4)$
$(2,2)$
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Why The midpoint is $\left(\frac{2+6}{2},\frac{4+8}{2}\right)=(4,6)$.
3
Multiple choice · Easy
Find the gradient of the line through $(1,2)$ and $(3,8)$.
$3$
$\frac{1}{3}$
$-3$
$2$
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Why Gradient $=\frac{8-2}{3-1}=\frac{6}{2}=3$.
4
Multiple choice · Easy
What is the gradient of the line $y=2x+5$?
$2$
$5$
$-2$
$\frac{1}{2}$
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Why In $y=mx+c$ the gradient is $m$, which is $2$ here.
5
Multiple choice · Easy
What is the $y$-intercept of the line $y=2x+5$?
$5$
$2$
$-5$
$\frac{1}{5}$
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Why In $y=mx+c$ the $y$-intercept is $c$, which is $5$ here.
6
Multiple choice · Easy
Find the midpoint of the segment joining $(-2,3)$ and $(4,7)$.
$(1,5)$
$(2,10)$
$(3,2)$
$(6,4)$
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Why The midpoint is $\left(\frac{-2+4}{2},\frac{3+7}{2}\right)=(1,5)$.
7
Fill in the blank · Easy
The gradient of the line $y=4x-7$ is
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Answer:
4
Why The coefficient of $x$ in $y=mx+c$ is the gradient, so $m=4$.
8
Fill in the blank · Easy
The $y$-intercept of the line $y=-3x+2$ is
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Answer:
2
Why The constant term $c$ in $y=mx+c$ is the $y$-intercept, so $c=2$.
9
Multiple choice · Easy
Which of these points lies on the $x$-axis?
$(5,0)$
$(0,5)$
$(0,-4)$
$(2,2)$
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Why A point lies on the $x$-axis when its $y$-coordinate is $0$, so $(5,0)$ is on the $x$-axis.
10
Multiple choice · Easy
A line is parallel to $y=3x+1$. What is its gradient?
$3$
$-\frac{1}{3}$
$1$
$-3$
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Why Parallel lines have equal gradients, so the gradient is $3$.
Key terms in Coordinate geometry
Coordinate: An ordered pair $(x, y)$ giving the position of a point on a plane.
Cartesian plane: A flat surface defined by two perpendicular axes used to locate points.
Origin: The point $(0, 0)$ where the $x$-axis and $y$-axis intersect.
X axis: The horizontal reference line on a coordinate grid.
Y axis: The vertical reference line on a coordinate grid.
Quadrant: One of the four regions of the coordinate plane divided by the axes.
Abscissa: The $x$-coordinate of a point, giving its horizontal position.
Ordinate: The $y$-coordinate of a point, giving its vertical position.
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