Question

A series of transformations shows how

¯¯¯¯¯¯¯¯¯¯¯
M
W
,
¯¯¯¯¯¯¯¯¯¯¯
M
K
,
and
¯¯¯¯¯¯¯¯¯¯¯
K
W
were translated, then rotated
90
∘
counterclockwise about point
X
to create
¯¯¯¯¯¯¯¯¯
X
G
,
¯¯¯¯¯¯¯¯
G
F
,
and
¯¯¯¯¯¯¯¯¯
F
X
.



Which of the following statements is true?

K
W
=
F
X
M
K
=
G
F
M
W
=
X
G
K
W
=
X
G

Answer 1

The true statement is KW = FX. This is the only statement that matches the given series of transformations.

In the given series of transformations, the line segments MW, MK, and KW are translated, then rotated 90° counterclockwise about point X to create the line segments XG, GF, and FX.

To determine which statement is true, let's analyze each option:

1. KW = FX: This statement is true. In the series of transformations, the line segment KW is translated and rotated to create the line segment FX.

2. MK = GF: This statement cannot be determined based on the given information. The question does not provide any details about the relationship between MK and GF.

3. MW = XG: This statement is false. In the given series of transformations, the line segment MW is translated and rotated to create the line segment XG, not MW.

4. KW = XG: This statement is false. In the series of transformations, the line segment KW is translated and rotated to create the line segment FX, not XG.

Therefore, the true statement is KW = FX. This is the only statement that matches the given series of transformations.