Question

check whether (5,-2),(6,4)&(7,-2) are points of isosceles triangle​

Answer 1

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Answer 2

The question is to check if the three points are the endpoints of an isosceles triangle.

So at first we have to find the length of each side of the triangle.

Therefore,

Let the points (5,-2),(6,4) and (7,-2) be the vertices of a triangle PQR.

We have to use the distance formula to determine the distance between the given points

Length of PQ= Distance between the points (5,-2) and(6,4).

PQ = √[(5-6)²+(-2-4)² ]= √[(-1)2+(-6)2]

PQ = √(1+36) =√37

Length of QR= Distance between (6,4) and (7,-2).

QR = √[(6-7)²+(4-(-2)² ]= √[(-1)²+(-6)²]

QR = √(1+36) =√37

Length of PR = distance between (5,-2) and (7,-2).

PR = √((5-7)2+(-2-2)2 )= √((-2)2+(0)2)

PR = √4 = 2

The sides PQ and QR are of the same length. Hence it is proved that the triangle PQR is an isosceles triangle.