Show that the points form the vertices of the indicated polygon. Right triangle: A(4, 0), B(2, 1), C(−1, −5)

BolkowN

BolkowN

Answered question

2020-12-06

Show that the points form the vertices of the indicated polygon.
Right triangle: A(4, 0), B(2, 1), C(−1, −5)

Answer & Explanation

lamusesamuset

lamusesamuset

Skilled2020-12-07Added 93 answers

Now evaluate AB, BC and CA:
AB =(24)2+(10)2
Using singdsitance formula (x2x1)2+(y2y1)2
AB =(2)2+(1)2
AB =4+1
AB =5
BC =(12)2+(51)2
Using singdsitance formula (x2x1)2+(y2y1)2
BC =(3)2+(6)2
BC =9+36
BC =45
CA =(4+1)2+(0+5)2
Using singdsitance formula (x2x1)2+(y2y1)2
CA =(5)2+(5)2
CA =25+25
CA =50
For a triangle ABC to be a right triangle it should satisfy Pythagoras theorem that is square of the longest side must be equal to the sum of the square of remaining of two sides. In above case the longest side is CA=50. So as
CA2=AB2+BC2
(50)2=(5)2+(45)2
50=5+45
50=50
Since right hand side is equal to left hand side.
So triangle ABC is a right angle triangle and the given three vertices forms a right triangle.
Hence given three vertices A(4, 0), B(2, 1) and C(−1, −5) forms a right triangle.

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