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

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

lamusesamuset · Accepted Answer

Now evaluate AB, BC and CA: AB =(2−4)2+(1−0)2 Using singdsitance formula (x2−x1)2+(y2−y1)2 AB =(−2)2+(1)2 AB =4+1 AB =5 BC =(−1−2)2+(−5−1)2 Using singdsitance formula (x2−x1)2+(y2−y1)2 BC =(−3)2+(−6)2 BC =9+36 BC =45 CA =(4+1)2+(0+5)2 Using singdsitance formula (x2−x1)2+(y2−y1)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.

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

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