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

The two vertices of ∆ABC are given by A(-3, 0) and B(-8, 5) and its

1.	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» 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).

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