Question

find the centroid of a triangle whose vertices are (3,4),(-7,-2),(10,6)​

Answer 1

Explanation:

The centroid of the triangle whose vertices are (3,-5),(-7,4),(10,-2) is

∵ The centroid of the triangle ABC = (x1 + x2 + x3 / 2 , (y1 + y2 + y3 / 2)

∴ The centroid of the triangle whose vertices A(3,-5), B(-7,4), C(10,-2) = (3-7+10 / 3 , -5 + 4 - 2 / 3)

= (2,-1)

Answer 2

$\red{\bold{\underline{Answer}}}$

$\green{\therefore{Centroid=(2,\frac{8}{3})}}$

$\pink{\bold{\underline{Step-by-step\:explanation}}}$

• Given

$\tt \implies Coordinate \: of \: p = (3,4) \\ \\ \tt \implies Coordinate \: of \: q= (-7,-2) \\ \\ \tt \implies Coordinate \: of \: r= (10,6)$

• To find

$\tt \implies Centroid = ?$

For finding value of centroid :

$\tt \implies x = \frac{ x_{1} + x_{2} + x_{3} }{3} \\ \\ \tt \implies x = \frac{3-7+10}{3} \\ \\ \tt \implies x = 2 \\ \\ \tt \implies y=\frac{ y_{1} + y_{2} + y_{3} }{3} \\ \\\tt \implies y= \frac{4-2+6}{3} \\ \\ \tt \implies y= \frac{8}{3} \\ \\ \green{\tt \therefore Centroid \: is \: (2,\frac{8}{3})}$