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# If the coordinates of the mid points of the sides of a triangle are (-1,-3),(2,1) and (4,5), find the coordinates of its vertices.ORShow that the points A(-2,5) , B(3,-4) and C(7,10) are the vertices of a right isosceles triangle.

Asked by Topperlearning User 4th June 2014, 1:23 PM

Let the vertices of the triangle be A(x1,y1), B(x2,y2) and C(x3,y3)

Let the given mid points of the sides BC, CA and AB be L(-1,-3), M(2,1) and N(4,5).

Now, by mid point formula,

-1 =

x2 + x3 = -2; x1 + x2 = 8; x1 + x3 = 4

2(x1 + x2 + x3) = 10

x1 + x2 + x3 = 5

On simplification,

x1 = 7, x2 = 1, x3 = -3

Similarly,

-3 =

y2 + y3 = -6; y1 + y3 = 2; y1 + y2 = 10

2 (y1 + y2 + y3) = 6

y1 + y2 + y3 = 3

y1 = 9, y2 = 1, y3 = -7

Hence, the three vertices of the triangle are (7,9), (1,1) and (-3,-7).

OR

The given points are A(-2,5) , B(3,-4) and C(7,10).

AB =

BC =

CA = =

Since, AB = AC, ABC is an isosceles triangle.

Also, AB2 + AC2 = 106+ 106 =212 = BC2

Since, AB2+AC2 = BC2, ABC is also a right triangle.

Hence, ABC is a right isosceles triangle.

Answered by Expert 4th June 2014, 3:23 PM
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