Points & Lines — practice questions

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

The points $A(0, 4)$, $B(6, 2)$ and $C(4, -4)$ form a triangle. Show that it is isosceles, giving exact side lengths, and state which vertex the equal sides meet at.

Find all points on the $y$-axis that are exactly 13 units from the point $A(5, 3)$, and explain why there are exactly two such points.

Find the midpoint of the segment joining $A(-4, 7)$ and $B(10, -3)$.

$M(4, -1)$ is the midpoint of $AB$, where $A$ is $(-3, 5)$. Find the coordinates of $B$, and verify your answer.

A triangle has vertices $A(1, 6)$, $B(7, 2)$ and $C(-1, -2)$. Show that the three medians of the triangle all pass through the point $G(\frac{7}{3}, 2)$, and state what you notice about the coordinates of $G$.

Find the gradient of the line through $(-1, 7)$ and $(3, -1)$.

Show that the points $P(-3, -5)$, $Q(0, 1)$ and $R(5, 11)$ are collinear, and explain why your method proves it.

The points $A(2, k)$, $B(5, 8)$ and $C(k, 20)$ are collinear. Find all possible values of $k$.