If the coordinates of the mid-points of the sides PQ and QR of \(\triangle PQR\) are \((-1, 8)\) and \((2, 4)\) respectively, then the length of PR is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 10
By the mid-point theorem, the segment joining the mid-points of two sides of a triangle is parallel to the third side and half its length. Let X \((-1, 8)\) be the mid-point of PQ and Y \((2, 4)\) the mid-point of QR; then PR \(=2\times\) XY.
Distance formula for XY: \(\text{XY}=\sqrt{(2-(-1))^2+(4-8)^2}=\sqrt{9+16}=5\)
PR is twice XY: \(\text{PR}=2\times5=10\)
