Question

The co-ordinates (5, - 2), (6, 4) and (7, - 2) are the vertices of an isosceles triangle.

• A. True
• B. False

Answer 1

The correct option is A True

Let the points (5, - 2), (6, 4), and (7, - 2) are representing the vertices A, B and C of the given triangle respectively.
$AB=\sqrt{{(5-6)}^2+{(-2-4)}^2}=\sqrt{{(-1)}^2+{\left(6\right)}^2}=\sqrt{1+36}=\sqrt{37}$
$BC=\sqrt{{(6-7)}^2+{(4-(-2))}^2}=\sqrt{{(-1)}^2+{\left(6\right)}^2}=\sqrt{1+36}=\sqrt{37}$
$CA=\sqrt{{(5-7)}^2+{(-2-(-2))}^2}=\sqrt{{(-2)}^2+0^2}=2$
Therefore, AB = BC
As two sides are equal in length, therefore, ABC is an isosceles triangle.