Question

select all the correct answers.
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?

• translate figure a down 4 units and left 6 units, and dilate it by a scale factor of 3.
• 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.
• reduce the measurement of each angle by half, and reflect the figure across the x - axis.
• reflect figure a across the y - axis, and dilate it by a scale factor of 4.

Explanation:

To determine which transformations result in a similar image to figure A, we recall that similar figures have the same shape (corresponding angles equal) and proportional sides (dilation with a scale factor, along with rigid transformations like translation, rotation, reflection).

Step 1: Analyze each option

• Option 1: Translate figure A down 4 units and left 6 units, and dilate it by a scale factor of 3.

Translation is a rigid transformation (preserves shape/angles), dilation scales sides proportionally. So this preserves similarity.

• Option 2: Double the measurement of each angle by 2, and dilate it by a scale factor of 2.

Changing angle measures (doubling) alters the shape, so not similar.

• Option 3: Increase the length of one side of figure A by 2 units, and rotate the figure 90° counterclockwise about its center.

Changing one side length (not proportional) breaks similarity, even with rotation.

• Option 4: Reduce the measurement of each angle by half, and reflect the figure across the x - axis.

Changing angle measures (halving) alters the shape, so not similar.

• Option 5: Reflect figure A across the y - axis, and dilate it by a scale factor of 4.

Reflection is a rigid transformation (preserves angles/shape), dilation scales sides proportionally. So this preserves similarity.

Answer:

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