if the pre image of a figure is located at (4,2) (-3,-3)(0,8) and it is reflected in the y-axis followed by a translation of 3 units left and 6 units down where is the new image locate give vertex coordinates
reflect: (x,y) -> (-x,y)
left: (x,y) -> (x-3,y)
down: (x,y) -> (x,y-6)
So, for all three,
(x,y) -> (-x,y) -> (-x-3,y) -> (-x-3,y-6)
(4,2) -> (-7,-4)
and so on
If the pre-image is located at (0,4), where would the image be located if you followed the translate (x+2, y-4)?
To find the new image after reflecting the pre-image in the y-axis followed by a translation, you can apply the following steps:
1. Reflecting in the y-axis:
- Reflect each point in the y-axis by changing the sign of the x-coordinate while keeping the y-coordinate unchanged.
- For the pre-image points (4, 2), (-3, -3), (0, 8), the reflected points would be (-4, 2), (3, -3), and (0, 8).
2. Translating 3 units left and 6 units down:
- For each reflected point, subtract 3 from the x-coordinate to move it 3 units left, and subtract 6 from the y-coordinate to move it 6 units down.
- The new image points would be: (-4-3, 2-6) = (-7, -4), (3-3, -3-6) = (0, -9), and (0-3, 8-6) = (-3, 2).
Therefore, the new image is located at the vertex coordinates (-7, -4), (0, -9), and (-3, 2).