Determine whether Triangle GHI is a right triangle for the given vertices.?

11. G(2,7) H(3,6) I(-4,-1)

12. G(-6,2) H(1,12) I(-2,1)

I forgot how to do these :P so help me pleaaase! I need answers by tomorrow thanks a lot in advance.

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  • 10 years ago
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    11)

    GH

    = H - G

    = (3,6) - (2,7)

    = (1,-1)

    HI

    = I - H

    = (-4,-1) - (3,6)

    = (-7,-7)

    IG

    = G - I

    = (2,7) - (-4,-1)

    = (6,8)

    If the triangle is a right triangle, the dot product between two of its vectors will produce zero.

    GH * HI

    = (1,-1) * (-7,-7)

    = (1)(-7) + (-1)(-7)

    = -7 + 7

    = 0

    Hence, GHI is a right triangle.

    12)

    GH

    = H - G

    = (1,12) - (-6,2)

    = (7,10)

    HI

    = I - H

    = (-2,1) - (1,12)

    = (-3,-11)

    IG

    = G - I

    = (-6,2) - (-2,1)

    = (-4,1)

    GH * HI

    = (7,10) * (-3,-11)

    = (7)(-3) + (10)(-11)

    = -21 -110

    = -131

    =/= 0

    HI * IG

    = (-3,-11) * (-4,1)

    = (-3)(-4) + (-11)(1)

    = 1

    =/= 0

    IG * GH

    = (-4,1) * (7,10)

    = (-4)(7) + (1)(10)

    = -18

    =/= 0

    Since none of the angles are right angles, GHI is not a right triangle.

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