2. Polygon ABCDEF is rotated °90°, reflected across the line y=−x, and then translated up 3 units and to the left 2 units to produce the image polygon A′B′C′D′E′F′. What are the coordinates of D′?
A. (−6,8)
B. (0,9)
C. (1,2)
D. (−4,1)
3. Polygon ABCDEF is reflected across the line y=−x, translated up 3 units and to the left 2 units, and then rotated 90° to produce the image polygon A′B′C′D′E′F′. What are the coordinates of D′?
A. (1,−7)
B. (−1,0)
C. (−5,−8)
D. (−6,−1)
4. Polygon ABCDEF is translated up 1 unit and to the right 4 units, rotated 90°, and then reflected across the line y=x to produce the image polygon A′B′C′D′E′F′. What are the coordinates of E′?
A. (6,1)
B. (9,−1)
C. (1,0)
D. (4,−4)
answer all of them
2. The coordinates of D are (-4, 1).
Explanation:
- To rotate a point 90 degrees counterclockwise, we swap its x and y coordinates and negate the new x coordinate. Therefore, the coordinates of D after rotating by 90 degrees are (-4, -2).
- To reflect across the line y=-x, we swap the x and y coordinates. Therefore, the coordinates of D after reflecting are (-2, -4).
- To translate up 3 units and left 2 units, we subtract 2 from the x-coordinate and add 3 to the y-coordinate. Therefore, the coordinates of D' are (-4, 1).
3. The coordinates of D′ are (-6, -1).
Explanation:
- To reflect across the line y=-x, we swap the x and y coordinates. Therefore, the coordinates of D after reflecting are (1, -4).
- To translate up 3 units and left 2 units, we subtract 2 from the x-coordinate and add 3 to the y-coordinate. Therefore, the coordinates of D after the first translation are (-1, -1).
- To rotate a point 90 degrees counterclockwise, we swap its x and y coordinates and negate the new x coordinate. Therefore, the coordinates of D' are (-6, -1).
4. The coordinates of E′ are (6, 1).
Explanation:
- To translate up 1 unit and right 4 units, we add 4 to the x-coordinate and 1 to the y-coordinate. Therefore, the coordinates of E after the first translation are (5, 1).
- To rotate a point 90 degrees counterclockwise, we swap its x and y coordinates and negate the new x coordinate. Therefore, the coordinates of E after rotating are (1, 5).
- To reflect across the line y=x, we swap the x and y coordinates. Therefore, the coordinates of E' are (5, 1), which corresponds to answer choice A.