What set of transformations could be applied to rectangle abcd to create a’b’c’d’?

a)reflected over the x-axis and rotated 180 degrees

b)reflected over the y-axis and rotated 180 degrees

c)reflected over the x-axis and rotated 90 degrees counterclockwise

d)reflected over the y-axis and rotated 90 degrees counterclockwise

C)Reflected over the x-axis and rotated 90 degrees counterclockwise

Step-by-step explanation:

Reflection over the x-axis move point C from (-1, 1) to (-1, -1), point D from (-1, 2) to (-1, -2), point A from (-4, 2) to (-4, -2) and point B from (-4, 1) to (-4, -1). As can be seen, y-coordinate changes sign, so that, the distance between the original point and its reflection respect x-axis remains the same.

Rotation 90 degrees counterclockwise around origin means that x-coordinate and y-coordinate switches and x-coordinate is multiplied by -1. So, point (-1, -1) transforms into (1, -1) - point C' -, (-1, -2) transforms into (2, -1) - point D' -, point (-4, -2) transforms into (2, -4) - point A' - and point (-4, -1) transforms into (1, -4) - point B'.

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°