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Given: The coordinates of iscosceles trapezoid JKLM are J(-b, c), K(b,c), L(a,0), and M(-a,0).
Prove: The diagonals of an isosceles trapezoid are congruent.
As part of the proof, find the length of KM

A) a2+b2+c2
B) (-a+b)2+c2
C) (a+b)2+c2

Respuesta :

The answer for this question is B. Let me know

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

       [tex]=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}[/tex]

Where, [tex](x_{1},y_{1}),(x_{2},y_{2})}[/tex] are coordinates of two points in the plane.

Length of Diagonal J L

                  [tex]=\sqrt{(a+b)^2+(0-c)^2}\\\\=\sqrt{(a+b)^2+c^2}[/tex]

Length of Diagonal K M

           [tex]=\sqrt{(a+b)^2+(0-c)^2}\\\\=\sqrt{(a+b)^2+c^2}[/tex]

So, we can see that,

  J L = KM  [tex]=\sqrt{(a+b)^2+(c)^2}[/tex]

Hence,The diagonals of an isosceles trapezoid are congruent.

So ,

  [tex]KM=\sqrt{(a+b)^2+c^2}[/tex]

Option C

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