Can someone please help me with this question. Thank you!

State the image of the given point after the following transformation:
(2,7) after a vertical stretch by a factor of 1/2 about the line y=1 followed by a horizontal stretch by a factor of 3 about the line x=3.

Sure! To find the image of a point after a sequence of transformations, we need to apply each transformation one by one in the given order.

First, let's understand what a vertical stretch by a factor of 1/2 about the line y=1 means. This transformation scales the y-coordinates of the point while keeping the x-coordinates the same. In this case, the line y=1 serves as the axis of the stretch. To perform this stretch, we need to multiply the y-coordinate of the given point by the stretch factor (1/2) while keeping the x-coordinate unchanged.

So, after the vertical stretch, the coordinates of the point (2,7) become (2, 7 * (1/2)) = (2, 3.5).

Next, we apply a horizontal stretch by a factor of 3 about the line x=3. This transformation scales the x-coordinates of the point while keeping the y-coordinates the same. The line x=3 serves as the axis of the stretch. To perform this stretch, we need to multiply the x-coordinate of the point by the stretch factor (3) while keeping the y-coordinate unchanged.

Hence, after the horizontal stretch, the coordinates of the point (2, 3.5) become ((2 * 3), 3.5) = (6, 3.5).

Therefore, the image of the given point (2,7) after the specified transformations is (6, 3.5).

To find the image of the point (2, 7) after the described transformations, we can follow these steps:

1. Vertical stretch by a factor of 1/2 about the line y = 1:
Since the line of reflection is y = 1, the distance between the point (2, 7) and the line y = 1 is 7 - 1 = 6 units.
Applying the vertical stretch by a factor of 1/2, the new distance becomes 6 * 1/2 = 3 units.
Since the point (2, 7) is above the line y = 1, the new image will be 3 units below the line y = 1.
Therefore, the new image after the vertical stretch is (2, 1 - 3) = (2, -2).

2. Horizontal stretch by a factor of 3 about the line x = 3:
Since the line of reflection is x = 3, the distance between the point (2, -2) and the line x = 3 is 2 - 3 = -1 unit.
Applying the horizontal stretch by a factor of 3, the new distance becomes -1 * 3 = -3 units.
Since the point (2, -2) is to the left of the line x = 3, the new image will be 3 units to the left of the line x = 3.
Therefore, the new image after the horizontal stretch is (2 - 3, -2) = (-1, -2).

The image of the point (2, 7) after the described transformations is (-1, -2).