Definition: When you reflect a point across the x-axis, the x-coordinate remains the same,
but the y-coordinate becomes opposite. The reflection of point (x, y) across the x-axis is (x, -y).

When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate becomes opposite. The reflection of point (x, y) across the y-axis is (-x, y).

Example: Find the coordinates of the figure if it is: a) reflected over the x-axis b) reflected over the y-axis

Solution: 

Determine the coordinates of the figure and use the rules for reflecting across the x and y axes to find the new coordinates.

Step 1: Determine the coordinates of the figure. The vertices of this triangle are at points (-4 , 6) (-4 , 2) and (2 , 6). We will use these coordinates to apply the rules for reflecting across the axes.

Step 2: For part a, reflecting across the x-axis, use the following rule: “the x-coordinate remains the same, but the y-coordinate becomes opposite” Applying this to our coordinates, (-4 , 6) (-4 , 2) and (2 , 6), gives us the new coordinates: (-4 , -6) (-4 , -2) (2 , -6)

So when the triangle is reflected across the x-axis, the new vertices become (-4 , -6) (-4 , -2) (2 , -6)

Step 3: For part b, reflecting across the y-axis, use the following rule: “the y-coordinate remains the same, but the x-coordinate becomes opposite” Applying this to our coordinates, (-4 , 6) (-4 , 2) and (2 , 6), gives us the new coordinates: (4 , 6) (4 , 2) (-2 , 6)

So when the triangle is reflected across the y-axis, the new vertices become (4 , 6) (4 , 2) (-2 , 6)

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