WAEC 2023 · Paper 1 · Q29

Name the triangle with the vertices $(1, -3)$ , $(6, 2)$ and $(0, 4)$ .

Worked solution (try it first)

Call the points $A(1, -3)$ , $B(6, 2)$ and $C(0, 4)$ , and find the squared side lengths.
$AB^2 = 5^2 + 5^2 = 50$ , $BC^2 = 6^2 + 2^2 = 40$ and $AC^2 = 1^2 + 7^2 = 50$ .
$AB = AC$ , so two sides are equal.
It is not right-angled, since $40 + 50 \ne 50$ and $50 + 50 \ne 40$ .
So it is an isosceles triangle, option A.