Question

figure a is a polygon that has been graphed on a coordinate grid. which of the following transformations will result in a similar image to figure a? reduce the measurement of each angle by half, and reflect the figure across the x - axis. double the measurement of each angle by 2, and dilate it by a scale factor of 2. increase the length of one side of figure a by 2 units, and rotate the figure 90° counterclockwise about its center. reflect figure a across the y - axis, and dilate it by a scale factor of 4. translate figure a down 4 units and left 6 units, and dilate it by a scale factor of 3.

Explanation:

Step1: Recall the properties of similar figures

Similar figures have the same shape (corresponding angles are equal) and their sides are in proportion (a dilation is a transformation that changes the size but not the shape of a figure). Reflections, rotations, and translations are rigid - motion transformations that preserve the shape and size (but dilation changes the size while keeping the shape if done correctly).

• For the first option: Reducing the measure of each angle by half changes the shape (since angles of similar polygons must be equal).
• For the second option: Doubling the measure of each angle changes the shape (angles of similar polygons must be equal).
• For the third option: Increasing the length of one side (while not changing others proportionally) changes the shape (sides of similar polygons must be in proportion).
• For the fourth option: Reflecting (a rigid - motion, preserves shape) and then dilating (changes size but keeps shape as long as all sides are scaled by the same factor).
• For the fifth option: Translating (a rigid - motion, preserves shape) and then dilating (changes size but keeps shape as long as all sides are scaled by the same factor).

Answer:

Reflect figure A across the y - axis, and dilate it by a scale factor of 4; Translate figure A down 4 units and left 6 units, and dilate it by a scale factor of 3.