The points (5, - 2), (6, 4) and (7, - 2) are the vertices of an ________ triangle.
A
equilateral
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B
isosceles
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C
scalene
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Solution
The correct option is B isosceles Let the points (5, - 2), (6, 4) and (7, - 2) represent the vertices A, B, and C of a triangle respectively.
Distance between the points is given by √(x1−x2)2+(y1−y2)2 BA=√(5−6)2+(−2−4)2 =√(−1)2+(6)2 =√1+36=√37 CB=√(6−7)2+(4−(−2))2 =√(−1)2+(6)2 =√1+36=√37 CA=√(5−7)2+(−2−(−2))2 =√(−2)2+02=2 ⇒ BA = CB
Two sides are equal in length.
So, ABC is an isosceles triangle.