Question

The points $(-2,2)$, $(8,-2)$ and $(-4,-3)$ are the vertices of a:

• A. equilateral $\Delta$
• B. isosceles $\Delta$
• C. right $\Delta$
• D. None of the above

Answer 1

The correct option is C right $\Delta$

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.