Question

If the (2,2)are coordinates of the centroid of a triangle whose vertices are (0,4),(-2,0) and (p, 2),then find the value of p​

Answer 1

Step-by-step explanation:

Solution:

Given vertices of a triangle are:

(x1, y1) = (0, 4)

(x2, y2) = (-2, 0)

(x3, y3) = (p, 2)

Centroid = (x, y) = (2, 2)

Using the centroid formula,

(x, y) = [(x1 + x2 + x3)/3, (y1 + y2 + y3)/3]

(2, 2) = [(0 – 2 + p)/3, (4 + 0 + 2)/3]

(2, 2) = [(p-2)/3, 6/3)]

Equating the x-coordinates,

(p – 2)/3 = 2

p – 2 = 2 × 3

p = 6 + 2

p = 8

Hence the value of p is 8