NDA 1 2024 Maths, question 62

Topic: Analytical geometry

Q62

$ABC$ is a triangle with $A(3,5)$ . The mid-points of sides $AB,AC$ are at $(-1,2),(6,4)$ respectively. What are the coordinates of centroid of the triangle $ABC$ ?

(a) $\left( \frac{8}{3},\frac{11}{3} \right)$
(b) $\left( \frac{7}{3},\frac{7}{3} \right)$ Correct answer
(c) $\left( 2,\frac{8}{3} \right)$
(d) $\left( \frac{8}{3},2 \right)$

Solution.

Answer: (b) $\left( \frac{7}{3},\frac{7}{3} \right)$

Reflect A = (3, 5) across the given midpoints to get B = 2(−1, 2) − (3, 5) = (−5, −1) and C = 2(6, 4) − (3, 5) = (9, 3).
The centroid is their coordinate average: (7/3, 7/3).