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Question
If the midpoints of the sides ofa triangle are (-2, 3), (4, -3), (4, 5), find its vertices.
Solution
Let P(x1, y1), Q(x2, y2 ) and R(x3, y3) be the coordinates of the vertices of .Δ PQR
Midpoint of PQ is D
D (-2 , 3) = D `(("x"_1 + "x"_2)/2 , ("y"_1 + "y"_2)/2)`
`("x"_1 + "x"_2)/2 = - 2 , ("y"_1 + "y"_2)/2 = 3`
X1 + X2 = -4 .....(1), Y1 + y2 = 6 .......(2)
similarly,
X2 + X3 = 8 ......(3), y2 + y3 = -6 ....(4)
X1+ X 3 = 8 ....(5), y1 +y3 = 10 ......(6)
Adding (1), (3) and (5)
2(x1 + x2 + x3 ) = 12
x1 + x2 + x3 = 6
- 4 + x3 = 6
x3 = 10
Adding (2), ( 4) and (6)
2(Y1+ Y2 + Y3) = 10
Y1+ Y2 + Y3 = 5
6 + Y3 = 5
Y3 = -1
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