Homework Help: math

Posted by ana on Friday, May 4, 2012 at 11:52pm.

The vertices of a triangle are listed below.
H(-2,4), I(22,4), J(10,-1)

Which of the following correctly classifies the triangle?
1.The triangle is an obtuse isosceles triangle.
2.The triangle is a right scalene triangle.
3.The triangle is an obtuse scalene triangle.
4.The triangle is a right isosceles triangle.

math - MathMate, Saturday, May 5, 2012 at 8:29am
Observe the coordinates of the vertices.
H and I are on the same horizontal line y=4, with x-coordinates -2 and 22 respectively.
The mid-point M between H and I is therefore (10,4).
The third point J(10,-1) is therefore directly below M, and JM is therefore a median and an altitude of the triangle, with a length of 4-(-1)=5, and ∠JMH=∠JMI=90°.
This tells us that JH=JI and therefore the triangle is isosceles.
Since JM<HI, ∠JIM < 90° which implies that the triangle is obtuse.

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