Question

If LA¯¯¯¯¯¯¯=−3x+4
𝐿
𝐴
¯
=
−
3
𝑥
+
4
and LK¯¯¯¯¯¯¯¯=−5x
𝐿
𝐾
¯
=
−
5
𝑥
, what value of LK¯¯¯¯¯¯¯¯
𝐿
𝐾
¯
would be required for LMKF
𝐿
𝑀
𝐾
𝐹
to be a rhombus?

(1 point)
Responses

20
20

2
2

10
10

−8

Answer 1

To determine the value of \( LK \) that would make the quadrilateral \( LMKF \) a rhombus, we start by noting that in a rhombus, all four sides must be of equal length.

We have:
- \( LA = -3x + 4 \)
- \( LK = -5x \)

For \( LMKF \) to be a rhombus, the lengths of \( LA \) and \( LK \) must be equal, thus we can set them equal to each other:

\[
-3x + 4 = -5x
\]

Now, let's solve for \( x \):

1. Rearranging the equation gives:
\[
-3x + 5x = -4
\]
\[
2x = -4
\]

2. Dividing both sides by 2 gives:
\[
x = -2
\]

Next, we substitute \( x = -2 \) back into the expressions for \( LA \) and \( LK \):

- For \( LA \):
\[
LA = -3(-2) + 4 = 6 + 4 = 10
\]

- For \( LK \):
\[
LK = -5(-2) = 10
\]

Thus, both \( LA \) and \( LK \) are equal to 10. Therefore, the value of \( LK \) required for \( LMKF \) to be a rhombus is:

**10**