Question

Name the type of triangle formed by the points A (2,-2), B (-2, 1), C (5, 2). Justify your answer ​

Answer 1

The three vertices of the triangle are A(−5,6),B(−4,−2) and (7,5).

By distance formula, AB = [(x2−x1)2+(y2−y1)2]

AB = [(−4−(−5))2+(4−(−2−6))2]

AB = [(1)2+(−8)2]

AB = [1+64]

AB = 65

By distance formula, AC = [(x2−x1)2+(y2−y1)2]

AC = [(7−(−5))2+(5−6)2]

AC = [(12)2+(−1)2]

AC = 144+1]

AC = 145

By distance formula, BC = [(x2−x1)2+(y2−y1)2]

BC = [(7−(−4))2+(5−(−2))2]

BC = [(11)2+(7)2]

BC = [121+49]

BC = 170

Length of all sides of the triangle are different.

So ABC is a scalene triangle.