Figure ABCD is reflected about the y-axis to obtain figure A′B′C′D′:
A coordinate plane is shown. Figure ABCD has vertices A at 2 comma 5, B at 1 comma 2, C at 3 comma 1, and D at 4 comma 5. Figure A prime B prime C prime D prime has vertices A prime at negative 2 comma 5, B prime at negative 1 comma 2, C prime at negative 3 comma 1, and D prime at negative 4 comma 5.
Which statement best describes the relationship between the two figures? (4 points)
Figure ABCD is similar to figure A′B′C′D′.
Figure ABCD is bigger than figure A′B′C′D′.
The measure of angle D is equal to the measure of angle A′.
The measure of angle D is equal to the measure of angle B′.
Figure ABCD is similar to figure A′B′C′D′.
The correct answer is:
Figure ABCD is similar to figure A′B′C′D′.
To determine the relationship between the two figures, we can compare their properties. In this case, the figures are obtained by reflecting figure ABCD about the y-axis.
First, let's compare the coordinates of the vertices of figure ABCD and figure A'B'C'D', keeping in mind that reflecting a point over the y-axis changes the sign of its x-coordinate:
A (2, 5) becomes A' (-2, 5)
B (1, 2) becomes B' (-1, 2)
C (3, 1) becomes C' (-3, 1)
D (4, 5) becomes D' (-4, 5)
Now, let's analyze the given statements:
1. Figure ABCD is similar to figure A'B'C'D': This statement is not correct because similar figures have proportional side lengths. In this case, the side lengths have different magnitudes, so the figures are not similar.
2. Figure ABCD is bigger than figure A'B'C'D': Since figure A'B'C'D' is obtained by reflecting figure ABCD about the y-axis, the sizes of the figures remain the same. Therefore, this statement is not correct.
3. The measure of angle D is equal to the measure of angle A': Although the figures are reflected, the angles do not change. So the measure of angle D in figure ABCD is equal to the measure of angle D' in figure A'B'C'D', not angle A'.
4. The measure of angle D is equal to the measure of angle B': This statement is correct because angle D in figure ABCD corresponds to angle B' in figure A'B'C'D'. When a figure is reflected about the y-axis, the orientation of angles across the y-axis is preserved.
Therefore, the correct statement is "The measure of angle D is equal to the measure of angle B'."
Which sequence of transformations creates a similar, but not congruent, triangle? (4 points)
Rotation and translation
Dilation and rotation
Reflection and rotation
Translation and reflection