Question

the vertices of a triangle are A(a, 0),B(0,b)and C(a,B)
Then the centroid of the triangle ABC, the mid point of AB, the mid point of BC and the mid point of AC is​

Answer 1

Step-by-step explanation:

$centroid \: of \: triangle \: = \: ( \frac{a + 0 + a}{3} \: \: \: \frac{0 + b + b}{3} ) \\ \\ = ( \frac{2a}{3} \: \: \: \: \frac{2b}{3} ) \\ \\ \\ \\ mid \: point \: of \: ab \: \: \: = \: \: ( \frac{a + 0}{2} \: \: \: \frac{b + 0}{2} ) \\ \\ = ( \frac{a}{2} \: \: \: \frac{b}{2} ) \\ \\ \\ \\ mid \: point \: of \: bc \: \: = ( \frac{0 + a}{2} \: \: \: \frac{b+ b}{2} ) \\ \\ = ( \frac{a}{2} \: \: \: \frac{2b}{2} ) \\ \\ = ( \frac{a}{2} \: \: \: b) \\ \\ \\ mid \: point \: of \: ca \: = \: ( \frac{a + a}{2} \: \: \: \frac{0 + b}{2} ) \\ = (a \: \: \: \frac{b}{2} )$