# 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.

Relevance
• 10 years ago

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.