Question

IF (- 3, 2), (1, - 2) and (5, 6) are mid-points of the
sides of a triangle. Find the co-ordinates of the
vertices of a triangle.
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Answer 1

Hope it helps u...thank you

Answer 2

$\boxed { \bf \: answer}$

Let P (-3,-2),Q(1,-2) & R(5,6) are mid points of sides of the triangle we have to find the coordinate of point A , B and C .

Using mid-point formula ,

$p( - 3,2) = \frac{a + p}{2} , \frac{b + q}{2} \\ so \: , \: \frac{a + p}{2} = - 3 \: and \: \frac{b + q}{2} = 2$

or a + p =-6 and b+ q =4........(¡)

similarly , a+x=10 & b+y =12.......(¡¡)

and p+x=2 and q+y=-4.....(¡¡¡)

subtracting a+x=10 from a+p=-6 we get x-p=-16

adding p+x=2 and x-p =-16

we get , 2x=-14

=> x=-17

therefore , p=9 And a=1

solving b+q=4 , b+y=12 and q+y=-4 we get y=2,b=10 and q=-6

therefore, coordinates of the triangle are (-7,-6),(9,2) and (1,10) .