Question

Pentagon ABCDE and Pentagon A''B''C'D''E are shown on the coordinate plane below.

which two transformations are applied to Pentagon ABCDE to create A"B"C"D"E"?

A) Translated according to the rule (x, y) → (x + 8, y + 2) and reflected across the y-axis

B) Translated according to the rule (x, y) → (x + 2, y + 8) and reflected across the x-axis

C) Translated according to the rule (x, y) → (x + 2, y + 8) and reflected across the y-axis

D) Translated according to the rule (x, y) → (x + 8, y + 2) and reflected across the x-axis​

Answer 1

C) Translated according to the rule (x, y) → (x + 2, y + 8) and reflected across the y-axis

Explanation:

We shift the whole Pentagon to the right by 2, then we slide it up by 8 (to create A'B'C'D'E'), and we reflect it across the y-axis to make A"B"C"D"E"

Proof Below:

Answer 2

D) Translated according to the rule (x, y) → (x + 8, y + 2) and reflected across the x-axis​

Explanation:

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, rotation, dilation and translation.

If a point X(x, y) is translated a units right and b units down, it new location is X'(x + a, y + b)

If a point X(x, y) is reflected across x axis, it new location is X'(x, -y)

Pentagon ABCDE is at A(-4, 5), B(-6, 4), C(-5, 1), D(-2, 2), E(-2, 4) while pentagon A"B"C"D"E" is at A"(4, -7), B"(2, -6), C"(3, -3), D"(6, -4), E"(6, -6)

If pentagon ABCDE is Translated according to the rule (x, y) → (x + 8, y + 2), the new points would be A'(4, 7), B'(2, 6), C'(3, 3), D'(6, 4), E'(6, 6). If a reflection across the x axis is the done, the new points are A"(4, -7), B"(2, -6), C"(3, -3), D"(6, -4), E"(6, -6)