Question

find the vertices of triangle, the mid point of the triangle are ( 2,1), (5,6),(-3,2).

Answer 1

Let the vertices of Trangle are ( x , y ) , ( a , b ) and ( d , e )

Now By using mid point theorem

(x + a)/2 = 2

x + a = 4 ... equation 1

(y + b)/2 = 1

y + b = 2 .... equation 2

(a +d)/2 = 5

a + d = 10... equation 3

(b +e)/2 = 6

b + e = 12... equation 4

(x + d)/2 = -3

x + d = -6.... equation 5

(y + e)/ 2 = 2

y + e = 4.... equation 6

Now, solve equation 1 and 5 we get

a - d = 10

a = 10 + d

Now, put value of a in equation 3

10 + d + d = 10

d = 0. and a = 10

S//y x = -6 , y = -3 , b = 5 and e = 7

So, the vertices of Trangle are

(-6 , -3 ) , ( 10 , 5 ) and ( 0 , 7 )

Have a nice day ahead.