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Mathematics

Find the co-ordinates of the centroid of ΔPQR whose vertices are P(6, 3), Q(-2, 5) and R(-1, 7).

Section Formula

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Answer

By using the centroid formula,

(x,y)=(x1+x2+x33,y1+y2+y33)(x, y) = \Big( \dfrac{x1 + x2 + x3}{3}, \dfrac{y1 + y2 + y3}{3} \Big)

P(6, 3), Q(-2, 5) and R(-1, 7)

Find the co-ordinates of the centroid of ΔPQR whose vertices are P(6, 3), Q(-2, 5) and R(-1, 7). Reflection, RSA Mathematics Solutions ICSE Class 10.

Substitute values we get:

⇒(x,y)=(6+(−2)+(−1)3,3+5+73)⇒(x,y)=(6−33,153)⇒(x,y)=(33,153)⇒(x,y)=(1,5).\Rightarrow (x, y) = \Big( \dfrac{6 + (-2) + (-1)}{3}, \dfrac{3 + 5 + 7}{3} \Big) \\[1em] \Rightarrow (x, y) = \Big( \dfrac{6 - 3}{3}, \dfrac{15}{3} \Big) \\[1em] \Rightarrow (x, y) = \Big( \dfrac{3}{3}, \dfrac{15}{3} \Big) \\[1em] \Rightarrow (x, y) = (1, 5).

Hence, coordinates of centroid of ΔPQR = (1, 5).

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