Coordinate Geometry

Find the midpoint of $A(3, 5)$ and $B(9, 5)$.

Find the midpoint of $C(4, 3)$ and $D(4, 11)$.

Find the gradient of the line through $(2, 1)$ and $(5, 10)$.

Find the gradient of the line through $(2, 10)$ and $(6, 2)$.

Find the distance between $(4, 5)$ and $(12, 5)$.

State the $y$-intercept of the line $y = 2x + -4$.

State the gradient of the line $y = -3x + 2$.

A line has gradient $3$ and $y$-intercept $-1$. Write the equation of the line.

Does the point $(4, 11)$ lie on the line $y = 3x + -1$?

Find $y$ when $x = 5$ on the line $y = -1x + 7$.

Find the distance between $(2, 3)$ and $(8, 11)$.

Find the exact distance between $(0, 0)$ and $(2, 5)$.

Find the midpoint of $(-6, 1)$ and $(4, -7)$.

Find the gradient of the line through $(-4, 2)$ and $(2, 14)$.

A line has gradient $2$ and passes through $(4, 3)$. Find its equation in the form $y = mx + c$.

Find the equation of the line through $(2, 1)$ and $(5, 10)$.

A line is parallel to $y = -2x + 3$. State its gradient.

A line is perpendicular to $y = 3x + -1$. State its gradient.

Rewrite the equation $3x + 2y = 12$ in the form $y = mx + c$.

Find the $x$-intercept of the line $y = 3x + -12$.

Find the exact distance between $(-1, -2)$ and $(5, 6)$.

What is the gradient of the line through $(5, 2)$ and $(5, 7)$?

Find the equation of the line through $(2, -3)$ that is parallel to the $x$-axis.

A line passes through $(6, 5)$ and is perpendicular to $y = 3x + -2$. Find its equation.

The midpoint of $AB$ is $(3, 6)$ where $A = (-1, 2)$. Find $B$.

Find the gradient of the line through $(1.5, 2)$ and $(4.5, 11)$.

Are the points $(1, 2)$, $(4, 5)$, and $(7, 8)$ collinear?

Find the equation of the line passing through $(6, 5)$ with gradient $-\dfrac{3}{4}$.

Find the point of intersection of $y = 3x + -2$ and $y = -1x + 6$.

$ABCD$ is a rectangle with $A(1, 2)$ and $B(4, 8)$. State the gradient of $CD$.

Find the equation of the perpendicular bisector of $A(1, 2)$ and $B(5, 14)$.

A triangle has vertices $A(0, 0)$, $B(8, 0)$, $C(0, 5)$. Show that $\triangle ABC$ is right-angled at $A$.

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

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

Three vertices of a parallelogram $ABCD$ are $A(1, 1)$, $B(5, 2)$, $C(6, 8)$. 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 $(0, 8)$ and $(6, 0)$. (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 $B$.