Question

Segment AB has endpoints A (-5, 7) and B (4, 4). The segment is reflected over the line y =4 to create endpoints A'B' and the rotated 90 degrees CW to form points A"B". Find the location of A" and B"a. A" (7, -13) B" (4, -4)b. A" (1, 5) B" (4, -4)c. A" (7, 3) B" (4, -4)d. A" (1, 5) B" (-4, 4)

Answer 1

b. A" (1, 5) B" (4, -4)

Step-by-step explanation:

Let's draw the segment AB and the line y = 4, so:

When we reflect over the line y = 4, the points will be at the same distance from the line y = 4 but on the opposite side. So, if A(-5, 7) is 3 units above y = 4, A' will be 3 units below y = 4. Therefore, the coordinate of A' are:

A'(-5, 1)

Because 4 - 3 = 1

On the other hand, B(4, 4) is at line y = 4, so its reflection is itself, so the coordinates of B' are:

B'(4, 4)

Now, if A'B' is rotated 90 degrees clockwise, we can use the following rule:

(x, y) ----> (y, -x)

So, the coordinates of A" and B" are:

A'(-5, 1) ----> (1, -(-5)) = A"(1, 5)

B'(4, 4) ----> (4, -4) = B"(4, -4)

Therefore, the answer is:

b. A" (1, 5) B" (4, -4)