Question

The three points (-2, 2), (8, -2) and (-4, -3) are the vertices of

• A. An isosceles triangle
• B. An equilateral triangle
• C. A right angled triangle
• D. None of these

Answer 1

Answer: (C)

A right angled triangle

Let $A(2,2),B(8,2)$ and $C(4,3)$
Distance between two points $(x_1,y_1)$ and $(x_2,y_2)$ can be calculated using the formula
$\sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2}$

Distance between the points A$(-2,2)$ and B $(8,-2)=\sqrt{{(8+2)}^2+{(-2-2)}^2}=\sqrt{100+16}=\sqrt{116}$

Distance between the points B$(8,-2)$ and C $(-4,-3)=\sqrt{{(-4-8)}^2+{(-3+2)}^2}=\sqrt{144+1}=\sqrt{145}$

Distance between the points A$(-2,2)$ and C $(-4,-3)=\sqrt{{(-4+2)}^2+{(-3-2)}^2}=\sqrt{4+25}=\sqrt{29}$

Since, ${\left(\sqrt{145}\right)}^2={\left(\sqrt{116}\right)}^2+{\left(\sqrt{29}\right)}^2$, the triangle is a right angled triangle.