find the third vertex of a triangle if its two, Mathematics

find the third vertex of a triangle if its two

Find the third vertex of a triangle if its two vertices are (-1, 4) and (5, 2) and mid point of one side is (0, 3). (Ans: (-5, 4) or (1, 2))

Ans : Let the third vertex be (x, y)

If (0,3) is mid point of BC then

x + 5/2 =0 (or) x = - 5

y + 2/2 =3 y=4. (-5, 4)

If (0,3) is mid point of AC then

x - 1/2 =0 x=1 y + 4/2 =3 y + 4 = 6 y = 2 (1, 2)

∴ (-5. 4) or (1, 2) are possible answers.

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