Point B(-3,7) is reflected across the line y=-x and then dilated with a scale factor of 3 and the center of dilation at the origin. What are the coordinates of point B" under the composition of transformations
under reflection in y = -x
(-3,7) ----> (-7,3)
with a dilation of 3 at the origin
(x,y) --->(3x,3y)
(-7,3) ----> (-21,9)
To find the coordinates of point B" under the composition of transformations, we need to follow these steps:
Step 1: Reflect point B(-3,7) across the line y=-x.
When we reflect a point across a line, its coordinates change by switching the x and y values. Therefore, the reflected point will have coordinates (7, -3).
Step 2: Dilate the reflected point with a scale factor of 3 and the center of dilation at the origin.
To dilate a point, we multiply its coordinates by the scale factor. In this case, the scale factor is 3. So, the coordinates of the dilated point, B", will be (3 * 7, 3 * -3), which simplifies to (21, -9).
Therefore, the coordinates of point B" under the composition of transformations are (21, -9).