Question

Reflect (4,-9) across the y-axis. Then reflect the result across the x-axis. What are the coordinates of the final point?

Answer 1

Answer: (-4,9)

Step-by-step explanation:

Answer 2

Answer:

(-4, 9)

Step-by-step explanation:

Here are the rules for reflections of points:

• Reflection across the y-axis: Multiply the x-values by -1
• Reflection across the x-axis: Multiply the y-values by -1

If you think about it, this makes sense because the y-axis is the vertical line of a rectangular coordinate system, so if you wanted to reflect points across the y-axis then you would have the have the x-values reflected over the same distance. The x-values determine whether the function moves left or right on the coordinate plane.

The x-axis is the horizontal line of the rectangular coordinate system, which would need the y-values to be opposites since they determine whether the function moves up or down on the coordinate plane.

If you can't remember the rule, then look at a coordinate plane and see what looks reasonable. Recall that a reflection across the y-axis needs the x-values to be opposites (positive and negative), and a reflection across the x-axis needs the y-values to be opposites.

If you wanted to reflect (4, -9) across the y-axis then the x-axis, just multiply both the x-value and y-value by -1 since you are trying to reflect the point across both axes.

• Reflection across the y-axis: (4, -9) ⇒ (4*-1, -9) ⇒ (-4, -9)
• Reflection across the x-axis: (-4, -9) ⇒ (-4, -9*-1) ⇒ (-4, 9)

I've attached pictures of what this reflection looks like on a graph. The original point is colored in blue and the final (reflected) point is colored in red.

You can see that the point was reflected across the y-axis then reflected over the x-axis. It could also work the other way around (doesn't matter which value you multiply by -1 first).