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).
