Q: Two lines have gradients $2$ and $-\frac{1}{2}$. What is the relationship between them?

Perpendicular — The product of the gradients is $2 \times \left(-\frac{1}{2}\right) = -1$, which is exactly the condition for two lines to be perpendicular.

Question 1

Find the midpoint of $A(2,4)$ and $B(6,10)$. Give as x,y.

Accepted Answer

4,7 — Midpoint $= \left(\frac{2+6}{2}, \frac{4+10}{2}\right) = (4,7)$.

Question 2

Find the gradient of the line through $A(2,4)$ and $B(6,10)$.

Accepted Answer

1.5 — $m = \frac{10-4}{6-2} = \frac{6}{4} = 1{,}5$.

Question 3

Two lines have gradients $2$ and $-\frac{1}{2}$. What is the relationship between them?

Accepted Answer

Perpendicular — The product of the gradients is $2 	imes \left(-\frac{1}{2}ight) = -1$, which is exactly the condition for two lines to be perpendicular.

Analytical Geometry

Sample practice questions