Question

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

Answer 1

The answer for this question is B. Let me know

Answer 2

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

`=√((a+b)^2+(0-c)^2)\\\\=√((a+b)^2+c^2)`

Length of Diagonal K M

`=√((a+b)^2+(0-c)^2)\\\\=√((a+b)^2+c^2)`

So, we can see that,

J L = KM
`=√((a+b)^2+(c)^2)`

Hence,The diagonals of an isosceles trapezoid are congruent.

So ,

`KM=√((a+b)^2+c^2)`

Option C