Question

using the section formula show that the points A(1,0),B(5,3),C(2,7)D(-2,4) are the vertices of a parallogram taken in order

Answer 1

Let A (-7 , 6)  B (8 , 5) and C (a , b) are the three vertices of the triangle.

centroid of the triangle = (1 , 3)              

Centroid of the triangle = (x1 + x2 + x3)/3 , (y1 + y2 + y3)/3

(1 , 3)  = (-7 + 8 + a)/3 ,(6 + 5 + b)/3

(1 , 3)  = (1 + a)/3 ,(11 + b)/3

Equating x and y coordinates

 (1+a)/3 = 1                       (11+b)/3 = 3

 1 + a = 3                          11 + b = 9

 a = 3 – 1                           b = 9 -11

 a = 2                                 b = -2

Therefore the missing vertex of the triangle is (2,-2)