Do the points represent the vertices of a right triangle (1,-4) (5,6) (-2,3)?

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Answer 1 · 2017-07-27T12:59:27

The #Delta# is an isosceles right triangle, right-angled at the pt.

#(-2,3).#

Let us name the given Points (pts.) #A,B, and, C,# resp.

We use the Notation #AB# to denote the Distance between

the pts. #A and B.#

Using the Distance Formula, we find that,

#AB^2=(1-5)^2+(-4-6)^2=16+100=116;#

#BC^2=(5+2)^2+(6-3)^2=49+9=58;# and,

#AC^2=(1+2)^2+(-4-3)^2=9+49=58.#

Clearly, #BC=AC, and, BC^2+AC^2=AB^2.#

Therefore, we conclude that, #DeltaABC# is an isosceles right

triangle, right-angled at the pt. #C.#