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Name the type of triangle formed by the points A(-5, 6), B(-4, -2) and C(7, 5).

Coordinate Geometry

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Answer

By distance formula,

Name the type of triangle formed by the points A(-5, 6), B(-4, -2) and C(7, 5). Coordinate Geometry, ML Aggarwal Understanding Mathematics Solutions ICSE Class 9.

d = (x2−x1)2+(y2−y1)2\sqrt{(x2 - x1)^2 + (y2 - y1)^2}

AB=[−4−(−5)]2+[−2−6]2=(−4+5)2+(−8)2=12+64=65.BC=[7−(−4)]2+[5−(−2)]2=112+72=121+49=170.AC=[7−(−5)]2+(5−6)2=122+(−1)2=144+1=145.AB = \sqrt{[-4 - (-5)]^2 + [-2 - 6]^2} \\[1em] = \sqrt{(-4 + 5)^2 + (-8)^2} \\[1em] = \sqrt{1^2 + 64} \\[1em] = \sqrt{65}. \\[1em] BC = \sqrt{[7 - (-4)]^2 + [5 - (-2)]^2} \\[1em] = \sqrt{11^2 + 7^2} \\[1em] = \sqrt{121 + 49} \\[1em] = \sqrt{170}. \\[1em] AC = \sqrt{[7 - (-5)]^2 + (5 - 6)^2} \\[1em] = \sqrt{12^2 + (-1)^2} \\[1em] = \sqrt{144 + 1} \\[1em] = \sqrt{145}.

Since, AB ≠ BC ≠ AC.

Hence, ABC is a scalene triangle.

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