Q. 10

The co-ordinates of mid-point s of sides of a triangle are (4, 3), (–2, 7) and (0, 11). Let us calculate the co-ordinates of its vertices.

Answer :

Let A(x1, y1), B(x2, y2), C(x3, y3) be the vertices of triangle and D(4, 3) be the mid-point of AB, E(–2, 7) be the mid-point of BC and F(0, 11) be the mid-point of AC.

And, we know mid-point formula, i.e. the coordinates of mid-point of line joining (x1, y1) and (x2, y2) is









x1 + x2 = 8, ………(1)


y1 + y2 = 6, ………(2)


x2 + x3 = – 4, ……..(3)


y2 + y3 = 14, …….(4)


x1 + x3 = 0, ……..(5)


y1 + y3 = 22 ………(6)


Now, adding (1) and (3), we get –


x1 + 2x2 + x3 = 4…..(7)


Now, subtracting (5) from (7), we get –


2x2 = 4


x2 = 2


Now, putting this in (3), we get –


2 + x3 = – 4


x3 = – 6


Now, putting this in (5), we get –


x1 – 6 = 0


x1 = 6


And now, adding (2) and (4), we get –


y1 + 2y2 + y3 = 20…..(8)


Now, subtracting (6) from (8), we get –


2y2 = – 2


y2 = – 2


Now, putting this in (4), we get –


– 2 + y3 = 14


y3 = 16


Now, putting this in (6), we get –


y1 + 16 = 22


y1 = 6


, A(x1, y1) = (6, 7), B(x2, y2) = (2, – 1), C(x3, y3) = (– 6, 15)


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