Translations/Dilations
Point P has coordinates (4, 6). Translate point P, 5 units to the left and 2 units down. Then dilate it by a scale factor of 4. What are the final coordinates of P''?
-4,16
Reflect the point (-2, -5) across the y-axis, then dilate the image using a scale factor of 2. What are the final coordinates of the point?
4,-10
A point A(4, -2) is rotated 180 degrees about the origin and then dilated by a scale factor of 0.5. What are the final coordinates of the point?
-2,1
A point is located at (5,-2). First, the point is translated 3 units up and 1 unit left. Then the translated point is dilated by a scale factor of 2. What is the x-coordinate of the final point?
8
Reflect the point (-4, 2) over the y-axis. Next, dilate the reflected point using a scale factor of 1/2. What is the new location of the point?
2,1
A pentagon has a vertex at (2, 3). It is rotated 270 degrees counter-clockwise about the origin, and then dilated by a factor of 2. What is the new coordinate of that vertex?
6,-4
Rectangle ABCD has vertices A(2, -1), B(6, -1), C(6, -3), and D(2, -3). Translate the rectangle 1 unit to the left and 4 units up. Next, dilate by a scale factor of 3. What are the coordinates of C''?
15,3
A square has vertices at (-1, -1), (1, -1), (1, 1), and (-1, 1). Reflect the square across the line y = x. Dilate the result by a scale factor of 3. What are the coordinates of the vertex that started at (1,1)?
3,3
A shape has a vertex at (-2, -2). The shape is rotated 180 degrees around the origin, and then dilated by a scale factor of 3. What is the coordinate of the vertex after these transformations?
6,6
Point T is located at (6, 3). Dilate T by a scale factor of 5 centered at the origin, then translate it 5 units to the left and 3 unit up. What are the final coordinates of T'?
25,18
Triangle GHI has vertices G(5, 1), H(6, 1), and I(6, 2). Dilate the triangle by a scale factor of 2 centered at the origin, then reflect it over the x-axis. What are the coordinates of G'?
-10,-2
A line segment has endpoints M(-1, 0) and N(0, 1). Rotate the segment 270 degrees clockwise about the origin, then dilate by a scale factor of 3. What are the coordinates of the new endpoints?
M'(0, -3), N'(3, 0)
Triangle ABC has vertices A(1, 2), B(3, 4), and C(5, 2). Translate the triangle 2 units to the left and 3 units up. Then, dilate the translated triangle by a scale factor of 2 with the origin as the center of dilation. What are the coordinates of A' after the translation and A'' after the dilation?
A'(-1, 5), A''(-2, 10)
Reflect the triangle with vertices A(1, 1), B(3, 1), and C(3, 4) across the y-axis. Then, dilate the reflected triangle by a scale factor of 0.5. What are the coordinates of the final image of vertex B?
(-1.5, 0.5)
A rectangle has vertices D(-2, -1), E(2, -1), F(2, 1), and G(-2, 1). Rotate the rectangle 90 degrees counterclockwise about the origin, then dilate by a scale factor of 1.5. What are the coordinates of the new vertices?
D'(1.5, -3), E'(1.5, 3), F'(-1.5, 3), G'(-1.5, -3)