Coordinate Geometry

Find the midpoint of $A(2, 4)$ and $B(8, 4)$.

Find the midpoint of $C(6, 2)$ and $D(6, 10)$.

Find the gradient of the line through $(1, 3)$ and $(4, 9)$.

Find the gradient of the line through $(1, 8)$ and $(5, 2)$.

Find the distance between $(2, 3)$ and $(9, 3)$.

State the $y$-intercept of the line $y = 3x + 5$.

State the gradient of the line $y = 4x + 7$.

A line has gradient $2$ and $y$-intercept $5$. Write the equation of the line.

Does the point $(3, 11)$ lie on the line $y = 2x + 5$?

Find $y$ when $x = 4$ on the line $y = 2x + 3$.

Find the distance between $(1, 2)$ and $(5, 5)$.

Find the exact distance between $(1, 1)$ and $(4, 5)$.

Find the midpoint of $(-3, 4)$ and $(5, -2)$.

Find the gradient of the line through $(-2, 3)$ and $(4, -3)$.

A line has gradient $3$ and passes through $(2, 5)$. Find its equation in the form $y = mx + c$.

Find the equation of the line through $(1, 3)$ and $(4, 9)$.

A line is parallel to $y = 4x + 7$. State its gradient.

A line is perpendicular to $y = 2x + 5$. State its gradient.

Rewrite the equation $2x + 1y = 6$ in the form $y = mx + c$.

Find the $x$-intercept of the line $y = 2x + -6$.

Find the exact distance between $(-3, 2)$ and $(5, -4)$.

What is the gradient of the line through $(3, 2)$ and $(3, 7)$?

Find the equation of the line through $(4, 7)$ that is parallel to the $x$-axis.

A line passes through $(4, 6)$ and is perpendicular to $y = 2x + 1$. Find its equation.

The midpoint of $AB$ is $(5, 4)$ where $A = (2, 1)$. Find $B$.

Find the gradient of the line through $(0.5, 1.5)$ and $(2.5, 5.5)$.

Are the points $(1, 2)$, $(3, 8)$, and $(5, 14)$ collinear?

Find the equation of the line passing through $(4, 3)$ with gradient $-\dfrac{2}{3}$.

Find the point of intersection of $y = 2x + 1$ and $y = -1x + 7$.

$ABCD$ is a rectangle with $A(1, 2)$ and $B(5, 5)$. State the gradient of $CD$.

Find the equation of the perpendicular bisector of $A(1, 2)$ and $B(7, 10)$.

A triangle has vertices $A(0, 0)$, $B(6, 0)$, $C(0, 4)$. Show that $\triangle ABC$ is right-angled at $A$.

Show that the triangle with vertices $A(0, 0)$, $B(6, 0)$, $C(3, 4)$ is isosceles. Find its area.

The points $(1, 3)$ and $(5, k)$ lie on a line with gradient $2$. Find $k$.

Three vertices of a parallelogram $ABCD$ are $A(1, 1)$, $B(5, 2)$, $C(7, 6)$. Find $D$.

In triangle $ABC$, $A(0, 0)$, $B(8, 0)$, $C(2, 6)$. Find the equation of the altitude from $C$ to $AB$.

For what value of $k$ are the points $(1, 2)$, $(3, k)$ and $(5, 14)$ collinear?

A point $P$ lies on the $x$-axis and is equidistant from $A(1, 4)$ and $B(7, 2)$. Find $P$.

A line passes through $(0, 6)$ and $(4, 0)$. (a) Find its equation. (b) Find the area of the triangle formed by the line and the axes.

A point $B$ is $5$ units from $A(2, 1)$ along the line $y = 0x + 1$. Find one possible position of $B$.