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math

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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 -

    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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