Question

The points $P(1,1),Q(-1.-1)$ and $R(-\sqrt{3},\sqrt{3})$ are the vertices of a triangle. The triangle is

• A. an isosceles triangle
• B. an equilateral triangle
• C. a scalene triangle
• D. none of the above

Answer 1

The correct option is B

an equilateral triangle

Given: $P(1,1),Q(-1.-1)$ and $R(-\sqrt{3},\sqrt{3})$ are the vertices of a triangle.

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

PQ = $\sqrt{(1-(-1){)}^2+(1-(-1{)}^2}=\sqrt{(2{)}^2+(2{)}^2}$ $=\sqrt{8}$ units

QR = $\sqrt{(-1+\sqrt{3}{)}^2+(-1-\sqrt{3}{)}^2}=\sqrt{(4-2\sqrt{3})+(4+2\sqrt{3})}$ $=\sqrt{8}$ units

PR = $\sqrt{(1+\sqrt{3}{)}^2+(1-\sqrt{3}{)}^2}=\sqrt{(4+2\sqrt{3})+(4-2\sqrt{3})}$ $=\sqrt{8}$ units

Since PQ = QR = PR, the triangle is an equilateral triangle.