Question

The vertices of a triangle are ( -3 , 3 ) , ( 5 , 3 ) and ( 1 , 6 ) . Prove that it is an isosceles triangle​

Answer 1

Step-by-step explanation:

let the ∆ be ∆ ABC

vertices of ∆ are A(-3,3) ,B(5,3) and C (1,6)

To proof ∆ ABC is an isosceles ∆,

distance of only two side should be equal.

so,to find distance between two points ,use this formula,AB=√(x2-x1)^2+(y2-y1)^2

Now,AB =√(5-(-3))^2+(3-3)^2)

=√8^2+0=√64=8

BC=√(1-5)^2+(6-3)^2=√(-4)^2+3^2=√16+9=√25=5

AC=√(-3-1)^2+(6-3)^2=√(-4)^2+3^2=√16+9=√25=5

Therefore BC=AC and not equal to AB

Hence ∆ABC is an isosceles∆