Question

Please help with 3 math questions ( 50 points )

1. Graph ΔABC with A(5, 1), B(-2, 6) C(-3, 4), and its image after a reflection along the x-axis. What are the coordinates of A'B'C'?

A'(-5, 1), B'(2, 6), C'(3, 4)

A'(1, -5), B'(6, 2), C'(4, 3)

A'(5, -1), B'(-2, -6), C'(-3, -4)

A'(1, 5), B'(6, -2), C'(4, -3)

A'(-5, -1), B'(2, -6), C'(3, -4)


2. Graph ΔXYZ with X(1, 2), Y(9, 7) Z(10, 1), and its image after a counterclockwise rotation of 90° about the origin. What are the coordinates of X'Y'Z'?


X'(-1, 2), Y'(-9, 7), Z'(-10, 1)


X'(1, -2), Y'(9, -7), Z'(10, -1)


X'(-1, -2), Y'(-9, -7), Z'(-10, -1)


X'(2, -1), Y'(7, -9), Z'(1, -10)


X'(-2, 1), Y'(-7, 9), Z'(-1, 10)


3. Graph parallelogram WXYZ with W(2, -3), X(-5, -1), Y(-1, 2), Z(6, 0), and its image after a translation of (x, y) → (x – 5, y + 2) What are the coordinates of W'?



(-3, -5)


(-3, -1)


(-3, 1)


(-5, 1)


(3, -5)

Answer 1

Explanation:

1. Reflection over the x-axis: (x, y) → (x, -y)

ΔABC with A(5, 1), B(-2, 6) C(-3, 4), after a reflection along the x-axis becomes A'(5, -1), B'(-2, -6) C'(-3, -4)

2. Counterclockwise rotation of 90° about the origin: (x, y) → (-y, x)

ΔXYZ with X(1, 2), Y(9, 7) Z(10, 1), after a counterclockwise rotation of 90° about the origin the coordinates are X'(-2,1) Y'(-7,9) Z'(-1,10)

3.

Parallelogram WXYZ with W(2, -3), X(-5, -1), Y(-1, 2), Z(6, 0), has the image after a translation of (x, y) → (x – 5, y + 2) as

W'(2-5, -3+2), X'(-5-5, -1+2), Y'(-1-5, 2+2), Z'(6-5, 0+2)

W'(-3, -1), X'(-10, 1), Y'(-6, 4), Z'(1, 2)

The coordinates of W'(-3, -1)

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