A triangle has points A(2, 3), B(2, 6), and C(7, 3) and is reflected over the x-axis and then over the line y = x. A"B"C" are the coordinates of the reflected image. What is the A" coordinate?

A(2,3) -- over x-axis--> A(2,-3) --- over y=x --> A(-3,2)

same thing for the other points

in general
(x,y) ---> (x, -y) ---> (-y,x)

To find the A" coordinate, we need to perform the given transformations.

Step 1: Reflection over the x-axis
When a point is reflected over the x-axis, we negate its y-coordinate. So, the reflected image of A(2, 3) over the x-axis is A'(2, -3).

Step 2: Reflection over the line y = x
To reflect a point over the line y = x, we swap its x-coordinate with its y-coordinate. Therefore, the reflected image of A'(2, -3) over the line y = x is A"( -3, 2).

Therefore, the A" coordinate is (-3, 2).

To find the A" coordinate, we need to perform the specified reflections on point A(2, 3).

First, let's reflect A over the x-axis. When a point is reflected over the x-axis, the y-coordinate changes sign while the x-coordinate remains the same. Point A(2, 3) reflected over the x-axis becomes A'(2, -3).

Next, we need to reflect A' over the line y = x. When a point is reflected over the line y = x, the x and y coordinates swap places. Point A'(2, -3) reflected over the line y = x becomes A"( -3, 2).

Therefore, the reflected image of point A(2, 3) is A"( -3, 2).