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If the midpoints of the sides of a trian...

If the midpoints of the sides of a triangle are `(2,1),(-1,-3),a n d(4,5),` then find the coordinates of its vertices.

Text Solution

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The correct Answer is:
`(7,9),(-3,-7),(1,1)`
Let the vertices of triangle be `(x_1,y_1),(x_2,y_2)`, and `(x_3,y_3)`. Then,
`(x_1+x_2)/(2)=2,(x_2+x_3)/(2),=-1,(x_3+x_1)/(2)=4`
Solving,we get `x_1=7,x_2=-3`, and `x_3=1`.
Similarly, `y_1=9,y_2=-7` and ` y_3=1`.
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