Quadrilateral L, Y, N, ULYNU can be mapped onto quadrilateral C, I, K, BCIKB by a rotation. If U, L, equals, 15UL=15, find K, BKB.

Question

Answer
Attempt 1 out of 2

K, BKB
be determined.

Answer 1

To solve the problem regarding the quadrilaterals L, Y, N, U and C, I, K, B and the relation between points U, L and points K, B, let’s break down the information we have.

Given that quadrilateral L, Y, N, U can be mapped onto quadrilateral C, I, K, B by a rotation, it means that the shapes are congruent and their corresponding sides and angles are equal due to the nature of rotation.

Now, we know that:

• U and L are points on quadrilateral L, Y, N, U
• The distance UL (which represents a side of the quadrilateral) equals 15 (notated as 15UL=15).

Since the mapping happens through a rotation, the corresponding points in quadrilateral C, I, K, B should maintain the same distances and angles. Therefore, if point U corresponds to point C and point L corresponds to point K, then we should have that:

• The length of segment CK in quadrilateral C, I, K, B should also equal the length of segment UL, meaning that \( CK = UL = 15 \).

From your question, if we denote \( K, B \) as a similar distance like \( C, I \) for the mapping, we can assert that \( KB \) must also equal 15.

Thus: Answer: \( K, BKB = 15 \).