Question

The two vertices of ∆ABC are given by A(-3, 0) and B(-8, 5) and its centroid is (-2, 1).What will be the coordinates of the third vertex C?

(a) (-5, -2)

(b) (5, 2)

(c) (-5, 2)

(d) (5, -2)

This question was addressed to me in examination.

My enquiry is from Geometry topic in division Coordinate Geometry of Mathematics – Class 10

Answer 1

Right answer is (d) (5, -2)

The best I can explain: The two vertices of triangle are A (-3, 0) and B (-8, 5). Its centroid is (-2, 1).

We know, xcentroid = \(\frac {x_1+x_2+x_3}{3}\) and ycentroid = \(\frac {y_1+y_2+y_3}{3}\)

Now, xcentroid = \(\frac {-3-8+x_3}{3}\)

xcentroid = -2

-2 = \(\frac {-3 – 8 + x_3}{3}\)

-6 = -3 – 8 + x3

5 = x3

Now, ycentroid = \(\frac {0+5+y_3}{3}\)

ycentroid = 1

1 = \(\frac {0 + 5 + y_3}{3}\)

3 = 5 + y3

-2 = y3

The third coordinate is (5, -2).