Distances & Areas — GCSE Maths practice questions

Question 1

A triangle has vertices $A(0, 0)$, $B(6, 0)$, $C(0, 4)$. Its area equals:

Accepted Answer

Base $= 6$, height $= 4$. Area $= \dfrac{1}{2} \cdot 6 \cdot 4 = 12$.

Answer

$6$

Answer

$10$

Answer

$12$

Answer

$24$

Question 2

The distance from the origin to the point $P(-3, 4)$ is:

Accepted Answer

$d = \sqrt{(-3)^2 + 4^2} = \sqrt{25} = 5$.

Answer

$1$

Answer

$5$

Answer

$7$

Answer

$25$

Question 3

The points $A(1, 2)$, $B(3, 6)$, $C(5, 10)$ are:

Accepted Answer

Area $= \dfrac{1}{2}\,|1(6 - 10) + 3(10 - 2) + 5(2 - 6)| = \dfrac{1}{2}\,|-4 + 24 - 20| = 0$. Hence collinear.

Answer

collinear

Answer

vertices of a right triangle

Answer

vertices of an isosceles triangle

Answer

vertices of an equilateral triangle

Question 4

The perimeter of the triangle with vertices $A(0, 0)$, $B(3, 0)$, $C(0, 4)$ is:

Accepted Answer

$|AB| = 3$, $|AC| = 4$, $|BC| = \sqrt{9 + 16} = 5$. Perimeter $= 3 + 4 + 5 = 12$.

Answer

$7$

Answer

$10$

Answer

$12$

Answer

$20$

Question 5

The area of the triangle with vertices $A(1, 1)$, $B(4, 5)$, $C(7, 2)$ is:

Accepted Answer

$	ext{Area} = \dfrac{1}{2}\,|1(5 - 2) + 4(2 - 1) + 7(1 - 5)| = \dfrac{1}{2}\,|3 + 4 - 28| = \dfrac{1}{2} \cdot 21 = \dfrac{21}{2}$.

Answer

$\dfrac{15}{2}$

Answer

$9$

Answer

$\dfrac{21}{2}$

Answer

$15$

Question 6

The distance between $A = (1, 2)$ and $B = (4, 6)$ is:

Accepted Answer

$AB = \sqrt{(4-1)^{2} + (6-2)^{2}} = \sqrt{9 + 16} = \sqrt{25} = 5$.

Answer

$4$

Answer

$5$

Answer

$7$

Answer

$\sqrt{25}$

Question 7

The midpoint of segment $AB$ where $A(2, 4)$ and $B(8, 10)$ is:

Accepted Answer

$M = \!\left(\dfrac{10}{2},\, \dfrac{14}{2}\right) = (5, 7)$.

Answer

$(3, 5)$

Answer

$(4, 6)$

Answer

$(5, 7)$

Answer

$(6, 14)$

Question 8

The distance between $A(1, 2)$ and $B(4, 6)$ is:

Accepted Answer

$d = \sqrt{(4 - 1)^2 + (6 - 2)^2} = \sqrt{9 + 16} = 5$.

Answer

$3$

Answer

$4$

Answer

$5$

Answer

$7$

Question 9

The area of a triangle with base $10$ and height $6$ is:

Accepted Answer

$A = \dfrac{1}{2} \cdot 10 \cdot 6 = 30$.

Answer

$60$

Answer

$30$

Answer

$16$

Answer

$15$

Question 10

The area of the rectangle with vertices $A(0, 0), B(5, 0), C(5, 3), D(0, 3)$ is:

Accepted Answer

Width $= 5$, height $= 3$. Area $= 15$.

Answer

$8$

Answer

$10$

Answer

$15$

Answer

$30$

Distances & Areas practice questions — GCSE Maths

Problems & worked solutions

Problem 1 — Distances & Areas

Problem 2 — Distances & Areas

Problem 3 — Distances & Areas

Problem 4 — Distances & Areas

Problem 5 — Distances & Areas

Problem 6 — Distances & Areas

Problem 7 — Distances & Areas

Problem 8 — Distances & Areas

Problem 9 — Distances & Areas

Problem 10 — Distances & Areas