Question

The points A (12, 8), B(-2, 6)and C(6,0) are vertices of

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

Answer 1

The correct option is A right angled triangle

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$(12,8)$ and B $(-2,6)=\sqrt{{(-2-12)}^2+{(6-8)}^2}=\sqrt{196+4}=\sqrt{200}$

Distance between the points B$(-2,6)$ and C $(6,0)=\sqrt{{(6+2)}^2+{(0-6)}^2}=\sqrt{64+36}=\sqrt{100}$

Distance between the points C$(6,0)$ and A $(12,8)=\sqrt{{(12-6)}^2+{(8-0)}^2}=\sqrt{36+64}=\sqrt{100}$

Since, ${AB}^2={BC}^2+{AC}^2$, the triangle is a right angled triangle.