Question

1. which transformation(s) produces an image that is congruent to the original figure?

rotation 90° clockwise about the origin
reflection over the x - axis
dilation with a scale factor of 2
translation 5 units to the right

Explanation:

Step1: Recall congruence transformations

Congruence transformations (rigid transformations) preserve the shape and size of a figure, so the image is congruent to the original. Rotations, reflections, and translations are rigid transformations. Dilation changes the size (unless scale factor is 1), so it's not a congruence transformation.

Step2: Analyze each option

• Rotation \(90^\circ\) clockwise: Rotation is a rigid transformation, so the image is congruent.
• Reflection over the \(x\)-axis: Reflection is a rigid transformation, so the image is congruent.
• Dilation with scale factor 2: Dilation scales the figure, changing its size, so not congruent.
• Translation 5 units right: Translation is a rigid transformation, so the image is congruent.

Answer:

Rotation \(90^\circ\) clockwise about the origin, Reflection over the \(x\)-axis, Translation 5 units to the right