Question

find the coordinates of the vertices of the triangle having mid points (-3,2) , (1,-2) and (5 , 6)​

Answer 1

Let coordinates of the vertices of the triangle A,B and C be 

A(x1,y1)B(x2,y2) and C(x3,y3), respectively.

Now, 2x2+x3=3⇒x2+x3=6.....(I)

2y2+y3=1⇒y2+y3=2......(II)

x3+x1=10.....(III)

y1+y3=12......(IV)

x1+x2=−6......(V)

y1+y2=4......(VI)

Adding equations (I), (III) and (V), we get

2x1+2x2+2x3=10

x1+x2+x3=5

x3=11       ....[∵x1+x2=−6]

x1=−1        ....[∵x2+x3=6]

∴x2=−5

Adding equations (II), (IV) and (VI), we get

2y1+2y2+2y3=18

y1+y2+y3=9

y3=5       ....[∵y1+y2=4]

y1=7        ....[∵y2+y3=2]

∴y2=−3

Therefore, the coordinates of the vertices are A(−1,7)B(−5,−3) and C(11,5).