TMUA · Paper 1: Applications of Mathematical Knowledge

Coordinate geometry

16 practice questions, each with the answer and an explanation.

Practise Coordinate geometry now

Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 16 questions

The line through $A (1, 3)$ and $B (4, 9)$ crosses the $x$ -axis at the point $(p, 0)$ . What is $p$ ?
$A$ is the point $(- 1, 2)$ and $B$ is the point $(5, 6)$ . The perpendicular bisector of $A B$ crosses the $y$ -axis at $(0, c)$ . What is $c$ ?
The circle $x^{2} + y^{2} - 6 x + 4 y - 3 = 0$ has radius $r$ . What is $r$ ?
A circle has centre $(4, 5)$ and radius $3$ . What is the shortest distance from the point $(1, 1)$ to the circle?
The line $y = x + k$ with $k > 0$ is a tangent to the circle $x^{2} + y^{2} = 8$ . What is $k$ ?
The line segment joining $(1, 2)$ and $(7, 10)$ is a diameter of a circle. Which of these points lies on the circle?
What is the area of the triangle with vertices $(0, 0)$ , $(6, 0)$ and $(2, 5)$ ?
The lines $y = 2 x + 1$ and $y = - x + 7$ meet at the point $P$ . What is the distance $O P$ , where $O$ is the origin?
The line through $(2, 3)$ parallel to $3 x + 2 y = 5$ has equation $3 x + 2 y = c$ . What is $c$ ?
The points $(0, 1)$ , $(2, 5)$ and $(5, k)$ lie on a straight line. What is $k$ ?
The line $3 x + 4 y = k$ with $k > 0$ meets the circle $x^{2} + y^{2} = 25$ at exactly one point. What is $k$ ?
The line $3 x + 4 y = 24$ meets the coordinate axes at $P$ and $Q$ . What is the area of triangle $O P Q$ where $O$ is the origin?
A circle has centre $(2, - 1)$ and passes through $(5, 3)$ . It meets the line $y = - 1$ at two points. How long is the chord between them?
What is the gradient of a line perpendicular to $5 x - 2 y = 7$ ?
The midpoint of $A B$ is $(3, - 1)$ and $A$ is the point $(5, 2)$ . What is the sum of the coordinates of $B$ ?
The point $P$ lies on the line $y = 2 x + 3$ and is the same distance from $(0, 0)$ and $(4, 0)$ . What is the $y$ -coordinate of $P$ ?

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