The coordinates of the vertices of ABC are A(-5, 1), B(-4, 5), and C(-2, 3). If the is first reflected over the y-axis and then over the x-axis, find the coordinates of A''.

To solve this problem, we need to understand how reflections over the y-axis and x-axis affect the coordinates of a point.

1. Reflection over the y-axis: The rule for a reflection over the y-axis is (x, y) → (-x, y). This means that the x-coordinate of the point changes its sign while the y-coordinate remains the same.

2. Reflection over the x-axis: The rule for a reflection over the x-axis is (x, y) → (x, -y). This means that the y-coordinate of the point changes its sign while the x-coordinate remains the same.

Now, let's apply these rules to point A(-5, 1).

Step 1: Reflect A over the y-axis. Using the rule (x, y) → (-x, y), we get A' = (-(-5), 1) = (5, 1).

Step 2: Reflect A' over the x-axis. Using the rule (x, y) → (x, -y), we get A'' = (5, -1).

So, the coordinates of A'' after the point A is first reflected over the y-axis and then over the x-axis are (5, -1).

To find the coordinates of A'' after the point is reflected over the y-axis and then over the x-axis, we need to follow these steps:

1. Reflect over the y-axis: The rule for a reflection over the y-axis is (x, y) → (-x, y). So, if we apply this rule to point A(-5, 1), we get A' = (5, 1).

2. Reflect over the x-axis: The rule for a reflection over the x-axis is (x, y) → (x, -y). So, if we apply this rule to point A'(5, 1), we get A'' = (5, -1).

So, the coordinates of A'' after the reflection over the y-axis and then over the x-axis are (5, -1).