Question

Given that the coordinate of the centroid is (8, 4) and coordinates of two vertices are
(6 ,6) and (10,8)find the coordinates of the third vertex. please answer properly

Answer 1

Given:

Coordinate of Centroid: (8,4)

Coordinates of two vertices:(6, 6) and (10,8)

To Find:

Coordinates of third vertex:?

Let the coordinates of third vertex be (x1, y1)

Answer:

Proceed using the following Centroid formulae:

$(8,4 ) =\big( \frac{x_1+x_2+x_3}{3}\big), \big( \frac{y_1+y_2+y_3}{3}\big) \\\\\sf Put ~the~ values~ of ~the~ coordinates. \\\\\sf (8,4 ) =\big( \frac{x_1+6+10}{3}\big), \big( \frac{y_1+6+8}{3}\big)\\\\\sf (8,4 ) =\big( \frac{x_1+16}{3}\big), \big( \frac{y_1+14}{3}\big)\\\\\sf Equating ~both ~the ~sides \\\\\sf 8= \frac{x_1+16}{3} \mapsto x_1+16=24 \mapsto x_1=24-16=8 \\\\\sf 4= \frac{y_1+14}{3} \mapsto y_1+14 = 12 \mapsto y_1=12-14 = - 2$

Hence, we got x1=8 and y1=-2

Coordinates of the third side is (8,-2)