Coordinate Geometry & Straight Lines Practice Questions

Work out the gradient of the line $AB$.

Write down the coordinates of the midpoint of $AB$.

Work out the gradient of the line.

Write down the coordinates of the point where the line crosses the $y$-axis.

Draw the line for values of $x$ from $-4$ to $6$.

Write down the coordinates of the point where the line crosses the $x$-axis.

Line $K$ has equation $2x + 5y = 30$

Line $L$ passes through the points $(-1, -4)$ and $(4, -6)$

Tick (✓) the correct statement about lines $K$ and $L$.

• The lines are parallel.
• The lines are perpendicular.
• The lines are neither parallel nor perpendicular.

Show working to support your answer.

Find the equation of the line parallel to $L$ that passes through $(2, 5)$.

Give your answer in the form $y = mx + c$.

Find the equation of the line perpendicular to $L$ that passes through $(8, -3)$.

Give your answer in the form $ax + by + c = 0$ where $a$, $b$ and $c$ are integers.

Work out the distance $PQ$.

Give your answer in the form $a\sqrt{b}$ where $a$ and $b$ are both integers greater than 1.

$R$ is the point on $PQ$ such that $PR : RQ = 1 : 2$

Work out the coordinates of $R$.

$A$ is the point $(2, -1)$ and $B$ is the point $(k, 5)$, where $k$ is a constant.

The length of $AB$ is $10$

Work out the two possible values of $k$.

Work out the coordinates of the point where the two lines intersect.

You must show your working.

Work out the coordinates of the point where the line $3x + 2y = 11$ crosses the $x$-axis.

Work out the equation of the line.

Give your answer in the form $y = mx + c$.

Show that the point $(7, -9)$ lies on this line.

Work out the equation of the perpendicular bisector of $AB$.

Give your answer in the form $y = mx + c$.

The perpendicular bisector of $AB$ crosses the $x$-axis at $P$ and the $y$-axis at $Q$.

$O$ is the origin.

Work out the area of triangle $OPQ$.

Show that triangle $ABC$ is right-angled.

Work out the area of triangle $ABC$.

Work out the coordinates of $D$.

Show that $ABCD$ is a rhombus.