Q. 23.5( 6 Votes )

# In this picture,

Answer :

Let the three coordinates of the larger triangle be (x1, y1), (x2, y2) and (x3, y3)

The three mid points on the three sides are (3, 3) , (4, 2) , (5, 4)

According to the section formula for mid points

x1 + x2 = 6 …Equation(i)

x2 + x3 = 8 …Equation (ii)

x3 + x1 = 10 …Equation(iii)

Solving Equation (i) ,(ii) and (iii)

x2 = 6 - x1

Putting this value in equation (ii) we get

x3 - x1 = 2 …Equation (iv)

Solving Equation (iii) & (iv)

2x3 = 12

x3 = 6

Putting in Equation (iv)

6 - x1 = 2

x1 = 4

Putting this value in equation (i)

4 + x2 = 6

x2 = 2

y1 + y2 = 6 …Equation (v)

y2 + y3 = 4 …Equation (vi)

y3 + y1 = 8 …Equation (vii)

Solving Equation (v) ,(vi) and (vii)

y2 = 6 - y1

Putting this value in equation (vi) we get

y3 - y1 = - 2 …Equation (viii)

Solving Equation (vii) & (viii)

2y3 = 6

y3 = 3

Putting in Equation (viii)

3 - y1 = - 2

y1 = 5

Putting this value in equation (v)

5 + y2 = 6

y2 = 1

The Vertices of the larger triangle are (4,5) , (2,1) , (6,3)

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