math
posted by ana on .
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.

Observe the coordinates of the vertices.
H and I are on the same horizontal line y=4, with xcoordinates 2 and 22 respectively.
The midpoint 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.