Coordinate Geometry (Edexcel GCSE Maths: Foundation): Exam Questions

$A$ is the point with coordinates $\left(3,5\right)$.
$B$ is the point with coordinates $\left(d,13\right)$.

The gradient of the line $AB$ is $2$.

Work out the value of $d$.

The point $A$ has coordinates (2, 3).
The point $B$ has coordinates (6, 8).

$M$ is the midpoint of the line $AB$.
Find the coordinates of $M$.

Point $A$ has coordinates (5, 8)
Point $B$ has coordinates (9, –4)

Work out the gradient of $AB$.

The point $A$ has coordinates (5, −4)
The point $B$ has coordinates (13, 1)

Work out the coordinates of the midpoint of $AB$.

Line $\mathbf{L}$ has equation $y=2-3x$
Write down the gradient of line $\mathbf{L}$.

$A$ is (2, 13) and $B$ is (10, 1)

Choose the midpoint of $AB$.

$P$ is (4, 9) and $Q$ is (–2, 1)
Choose the midpoint of $PQ$.

Work out the gradient of the straight line through (–2, 3) and (1, 9)

Point $C$ is the midpoint of points $A\left(3,-3\right)$ and $B\left(4,9\right)$.

Determine the coordinates of point $C$.

The midpoint $M$ of another line segment $PQ$ is $M\left(-3,-4\right)$.

Given the point $P\left(-8,2\right)$, work out the coordinates of point $Q$.

Find the gradient of the line from $P\left(-3,-4\right)$ to $Q\left(3,4\right)$.

Write your answer as a mixed number in simplest form.

Write down the coordinates of point A.

ABCD is a parallelogram.

On the grid, mark with a cross ($\times$) the point D so that ABCD is a parallelogram.

Write the coordinates of the midpoint of the line segment AC.

The coordinates $A$, $B$ and $C$ are such that $ABC$ is a straight line.

The coordinates of $A$ are $\left(2,-6\right)$

The coordinates of $C$ are $\left(18,2\right)$

Given that $AB:BC=3:5$, find the coordinates of $B$.

Find the gradient of the straight line with equation  $5x+2y=7$.

The diagram shows an octagon

$x=1$and $y=5$ are lines of symmetry.

Work out the coordinates of point $Q$.

A straight line is drawn on the centimetre grid.

Fay assumes that the scale is 1 cm represents 1 unit.

Use her assumption to work out the gradient of the line.

In fact, the scale is 1 cm represents 2 units.

Which statement is correct? Tick one box.

$\square$      The answer to part (a) is too big

$\square$        The answer to part (a) stays the same

$\square$        The answer to part (a) is too small

$A$ is the point (—1, 2)
$B$ is the point (7, 5)

Find the coordinates of the midpoint of $AB$.

$P$ is the point (—4, 4)
$Q$ is the point (1, —5)

Find the gradient of $PQ$.

Point $P$ has coordinates (5, 7).
Point $M$ has coordinates (1, 2.5).

Point $M$ is the midpoint of the line $PQ$.

Find the coordinates of point $Q$.

Point $A$ has coordinates $(–3,11)$
Point $B$ has coordinates $(47,b)$
The midpoint of $AB$ has coordinates $(a,–19)$

Find the value of $a$ and the value of $b$.

a = ................................................ 
b = ................................................