Question

The centroid of the triangle formed by the
vertices (7,p), (q, -6) and (10,10) is
(6,4) then (p, q) is​

Answer 1

Step-by-step explanation:

7+q+10/3=6

17+q =18

q = 1

p+(-6) + 10/3 = 4

p-6+10 /3 =4

p+4 =12

p= 8

Answer 2

We have three coordinates of the vertices of the triangle as, P(7,p) , Q(q, -6) , R(10,10)

Also, The coordinate of the centroid of this triangle is (6,4) and we have to find (p,q).

We have,

• P(x₁, y₁) = 7, p
• Q(x₂, y₂) = q, -6
• R(x₃, y₃) = 10, 10

We know, The coordinate of centroid of a triangle which has its three vertices of which the coordinates are (x₁, y₁) (x₂, y₂) and (x₃, y₃) is given by:

⇒ (x, y) = { (x₁ + x₂ + x₃) / 3 , (y₁ + y₂ + y₃) / 3 }

Here, x = 6 and y = 4,

⇒ Abscissa, x = (x₁ + x₂ + x₃) / 3

⇒ 6 = (7 + q + 10) / 3

⇒ 18 = 17 + q

⇒ q = 1

Similarly,

⇒ Ordinate, y = (y₁ + y₂ + y₃) / 3

⇒ 4 = (p + (-6) + 10) / 3

⇒ 12 = p + 4

⇒ p = 8

Here, The values of p and q are 8 & 1, respectively.

∴ (p, q) = (8, 1)