Question

1. tyrell transformed a figure contained in quadrant iv by reflecting it over the y - axis and rotating it ( 180^{circ} ) clockwise. which of the following is a true statement?

a. the image is congruent to the pre - image.
b. the image is contained in quadrant iii.
c. both a and b are true.
d. neither a nor b is true.

Explanation:

Step1: Analyze reflection and rotation properties

Reflection over the \(y -\)axis and rotation \(180^{\circ}\) are rigid transformations. Rigid transformations preserve the shape and size of the figure, so the image is congruent to the pre - image.

Step2: Analyze the quadrant of the image

Let \((x,y)\) be a point in quadrant IV (\(x>0,y < 0\)).

• Reflection over the \(y -\)axis: The rule is \((x,y)\to(-x,y)\).
• Rotation \(180^{\circ}\) clockwise: The rule is \((a,b)\to(-a,-b)\). If we first reflect \((x,y)\) (\(x > 0,y<0\)) over the \(y -\)axis to get \((-x,y)\) and then rotate \(180^{\circ}\) clockwise, we get \((x, - y)\). Since \(x>0\) and \(-y>0\) (because \(y < 0\)), the image is in quadrant I.

Answer:

A. The image is congruent to the pre - image.