Question

prove that the points (-2,-2),(-1,2) and (3,1) are the vertices of an isosceles triangle​

Answer 1

By using the distance formula,

d=√(x2-x1)²+(y2-y1)²

d1=√(-1-(-2))² + (2-(-2))²

d1=√(-1)²+(4)²

d1=√1+16

d1=√17...(For AB)(1)

d2=√(3-(-1))²+(1-2)²

d2=√(4)²+(-1)²

d2=√16+1

d2=√17...(For BC)(2)

d3=√(-2-3)²+(-2-1)²

d3=√(5)²+(3)²

d3=√25+9

d3=√34...(For CA)(3)

Since the sides (1) and (2) are the same and (3) is different, just like in an isoceles triangle,

Hence, the points (-2,-2),(-1,2) and (3,1) are the vertices of an isoceles triangle.

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