Question

(5, -2), (6, 4) and (7, -2) are the vertices of a ........ triangle.

• A. equilateral
• B. right angle
• C. scalene
• D. isosceles

Answer 1

The correct option is D isosceles

We can use the distance formula to find the length of the three sides and then check if the triangle is isosceles.

Distance between points=$\sqrt{{(x_2-x_1)}^2+{(y_2-y_1)}^2}$

Distance AB $=\sqrt{{(6-5)}^2+{(4+2)}^2}=\sqrt{37}$

Distance BC $=\sqrt{{(7-6)}^2+{(-2-4)}^2}=\sqrt{37}$

Distance CA $=\sqrt{{(7-5)}^2+{(-2+2)}^2}=\sqrt{4}$

We find distances $AB=BC$ and hence, the triangle is isosceles.