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Rebecca draws two triangles on this coordinate plane.

She wants to find a sequence of transformations that will map triangle A B C onto triangle A" B" C". She starts by rotating triangle A B C ninety degrees clockwise about the origin to form triangle triangle A' B' C'.

a. What are the coordinates of point B prime under this rotation?

Rebecca maps triangle A prime B prime C prime onto triangle A double prime B double prime C double prime using the transformation (x, y) maps to (x + h, y + k).

a. What are the values of h and k?

Rebecca wants to find a sequence of transformations that uses only reflections to map triangle A B C onto triangle A" B" C". The first reflection that she uses is a reflection across y = -x.

a. What are the coordinates of point A''' after this reflection?

b. Identify the second reflection Rebecca must perform in order to map triangle A B C onto triangle A" B" C".

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Answer:

The answer is below

Step-by-step explanation:

From the image attached, the coordinates of triangle ABC are at A(-5, 4), B(-5,7) and C(-2, 7)

a) If a point O(x,y) is rotated 90° clockwise, the new coordinate is O'(y, -x)

If triangle ABC is rotated 90° clockwise, its new coordinate is at:

A'(4, 5), B'(7, 5) and C'(7, 2)

The coordinate of A"B"C" is A"(2,5), B"(5,5), C(5,2)

Hence the transformation used to map A'(4, 5), B'(7, 5) and C'(7, 2) to A"(2,5), B"(5,5), C(5,2) is (x - 2, y + 0). Hence comparing with (x + h, y + k) gives:

h = -2, k = 0

b) If a point O(x,y) is reflected across the y = -x line, the new coordinate is O'(-y, -x)

If triangle ABC is reflected across y = -x, its new coordinate is at:

A'(-4, 5), B'(-7, 5) and C'(-7, 2)

The coordinate of A"B"C" is A"(2,5), B"(5,5), C(5,2)

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