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.

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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