Question

Two vertices of a triangle are the points (1, 4) and (7, 2). Its centroid is the point (5, 3), then the third vertex is :

• A. (3, 7)
• B. (7, 3)
• C. (1, 1)
• D. (0, 0)

Answer 1

Answer: (B)

(7, 3)

Centroid of a triangle with vertices
${(x}_1,y_1);{(x}_2,y_2)$ and ${(x}_3,y_3)$ is calculated by the formula $(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3})$

Let the third vertex of the triangle be $(x,y)$
So, centroid $=(\frac{1+7+x}{3},\frac{4+2+y}{3})=(5,3)$
$=(\frac{8+x}{3},\frac{6+y}{3})=(5,3)$
$=>8+x=15;6+y=9$
$x=7;y=3$
Hence the third vertex of the triangle is $(7,3)$