Question

Given: The coordinates of iscosceles trapezoid JKLM are J(-b, c), K(b,c), L(a,0), and M(-a,0).

Answer 1

Answer with explanation:

It is given that, coordinates of Isosceles trapezoid J K L M are J(-b, c), K(b,c), L(a,0), and M(-a,0).

To Prove: The diagonals of an isosceles trapezoid are congruent.

Proof:

  Distance formula , that is distance between two points in x y plane is given by

       $=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}$

Where, $(x_{1},y_{1}),(x_{2},y_{2})}$ are coordinates of two points in the plane.

Length of Diagonal J L

                  $=\sqrt{(a+b)^2+(0-c)^2}\\\\=\sqrt{(a+b)^2+c^2}$

Length of Diagonal K M

           $=\sqrt{(a+b)^2+(0-c)^2}\\\\=\sqrt{(a+b)^2+c^2}$

So, we can see that,

  J L = KM  $=\sqrt{(a+b)^2+(c)^2}$

Hence,The diagonals of an isosceles trapezoid are congruent.

So ,

  $KM=\sqrt{(a+b)^2+c^2}$

Option C

Answer 2

The answer for this question is B. Let me know