Triangle ABC is graphed on the grid below.

If triangle ABC is translated up 3 units and then reflected across the x-axis to
create Δ A"B"C" what will be the approximate length of A"B" ?

A. About 20
Incorrect. Remember translations and reflections are congruence transformations.

B. About 11.4
Correct! You found the length of AB and remembered that translations and reflections are congruence transformations.

C. About 5
Incorrect. You remembered that translations and reflections are congruence transformations but you found the length of BC.

D. About 10.6
Incorrect. You remembered that translations and reflections are congruence transformations but you found the length of AC.

Point A has coordinates (x, y). Point A is translated down 3 units then reflected across the line y = x to create point A" Which best describes the coordinates of point A"?

A. (y − 3,  x)
Correct! A translation down reduces the y-coordinate and a reflection across the line y = x interchanges the x and y-coordinates.

B. (y + 3, x)
Incorrect. A translation down reduces the y-coordinate and a reflection across the line y = x interchanges the x and y-coordinates.

C. (3 – y, -x)
Incorrect. A translation down reduces the y-coordinate and a reflection across the line y = x interchanges the x and y-coordinates.

D. (-y – 3, -x)
Incorrect. A translation down reduces the y-coordinate and a reflection across the line y = x interchanges the x and y-coordinates.

Triangle ABC is graphed on the grid below.

If a 90° rotation about the origin is applied to triangle ABC is to create Δ A'B'C' what will be the coordinates of A'?

A. (1, -3)
Incorrect. A 90° rotation about the origin changes the point (x, y) to (-y, x).

B. (-1, 3)
Incorrect. A 90° rotation about the origin changes the point (x, y) to (-y, x).

C. (3, 1)
Incorrect. A 90° rotation about the origin changes the point (x, y) to (-y, x).

D. (-3, 1)
Correct! A 90° rotation about the origin changes the point (x, y) to (-y, x).

James is creating a logo for his new business. He started his design by graphing a rectangle on a coordinate grid. Next he reflected the rectangle across the y-axis and then translated it upward 3 units. If his original rectangle had the following coordinates: (2, -2), (2, -7), (8, -2), (8, -7). What are the coordinates of the new rectangle?

A. (2, 1), (2, -4), (8, 1), (8, -4)
Incorrect. A reflection across the y-axis will change the x-coordinate to its opposite and a translation up 3 units will increase the y-coordinate by 3.

B. (-2, -1), (-2, 4), (-8, -1), (-8, 4)
Incorrect. A reflection across the y-axis will change the x-coordinate to its opposite and a translation up 3 units will increase the y-coordinate by 3.

C. (-2, 1), (-2, -4), (-8, 1), (-8, -4)
Correct! A reflection across the y-axis will change the x-coordinate to its opposite and a translation up 3 units will increase the y-coordinate by 3.

D. (1, -2), (-4, -2), (1, -8), (-4, -8)
Incorrect. A reflection across the y-axis will change the x-coordinate to its opposite and a translation up 3 units will increase the y-coordinate by 3.