Question

show that the following points are the vertices of a right angled isooceles triangle (1,2),(1,5)and(4,2)

Answer 1

Heya !!!




Let given points are A(1,2) , B(1,5) and C(4,2)






A(1,2) and B(1,5)


Here,




X1 = 1 , Y1 = 2 and X2 = 1 , Y2 = 5






AB² = (X2-X1)² + (Y2-Y1)²




AB² = (1-1)² + (5-2)²




AB² = 9





AB = root 9 = 3




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A(1,2) and C(4,2)




Here,



X1 = 1 , Y1 = 2 and X2 = 4 , Y2 = 2





AC² = (X2-X1)² + (Y2-Y1)²






AC² = ( 4 - 1)² + (2-2)²





AC² = 9




AC = root 9 = 3





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B(1,5) and C(4,2)






Here,.





X1 = 1 , Y1 = 5 and X2 = 4 , Y2 = 2





BC² = (X2-X1)² + (Y2-Y1)²



BC² = (4-1)² + (2-5)²




BC² = (3)² + (-3)²





BC² = 18




BC = root 18





Here,



We can see that the two sides of triangle ABC are equal and one side is different.




Hence,



∆ABC is an Isosceles triangle.





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