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Question

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

A

Right-angled triangle

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B

Isosceles triangle

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C

Scalene triangle

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D

Equilateral triangle

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Solution

## The correct option is C Scalene triangle To find the type of triangle, first, we determine the length of all the three sides and see if the condition of the triangle is satisfied by these sides. Now, using distance formula between two points, AB=√(−4+5)2+(−2−6)2=√(1)2+(−8)2=√1+64=√65 [∵d=√(x2−x1)+(y2−y1)2]BC=√(7+4)2+(5+2)2=√(11)2+(7)2=√121+49=√170And CA=√(−5−7)2+(6−5)2=√(−12)2+(1)2√144+1=√145 We see that, AB≠BC≠CA And Δ ABC does not satisfy Pythagoras theorem Hence, the required triangle is scalene because all sides are of different length.

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