Question

If the images of the points A(1, 3), B(3, 1) and C(2, 4) in the line x + 2y = 4 are D, E and F respectively, then the centroid of the triangle DEF is

(1) (3, -1)

(2) \(\left(-\frac{3}{5},-\frac{2}{5}\right)\)

(3) \(\left(\frac{2}{5},-\frac{1}{5}\right)\)

(4) \(\left(\frac{1}{5},-\frac{2}{5}\right)\)

Answer 1

Correct option is (3) \(\left(\frac{2}{5},-\frac{1}{5}\right)\)

Centroid of the \(\triangle D E F\) is the mirror image of the centroid of the \(\triangle A B C\) about the line \(x+2 y=4.\)

\(G_1=\) Centroid of \(\triangle A B C=(2,3), G_2=\) Centroid of \(\triangle D E F.\)