Question

the point a is shown below. reflect a across the x - axis. then reflect the result across the y - axis. plot the final point. important: only plot the final point in your answer.

Explanation:

Step1: Find coordinates of A

Point A is on the y - axis, so its coordinates are $(0, 6)$.

Step2: Reflect across x - axis

The rule for reflecting a point $(x,y)$ across the x - axis is $(x,-y)$. So reflecting $A(0,6)$ across the x - axis gives $(0,-6)$.

Step3: Reflect across y - axis

The rule for reflecting a point $(x,y)$ across the y - axis is $(-x,y)$. Reflecting $(0,-6)$ across the y - axis gives $(0,-6)$? Wait, no. Wait, the first reflection: $(0,6)$ across x - axis is $(0, - 6)$. Then reflecting $(0,-6)$ across y - axis: since x is 0, -x is 0, so the point is $(0,-6)$? Wait, no, maybe I made a mistake. Wait, original point A: looking at the graph, A is at (0,6). Reflect across x - axis: (x,y)→(x, - y), so (0,6)→(0, - 6). Then reflect (0,-6) across y - axis: (x,y)→(-x,y), so (0,-6)→(0,-6). Wait, but that seems odd. Wait, maybe I misread the graph. Wait, no, the x - axis reflection: (0,6) becomes (0,-6). Then y - axis reflection: (0,-6) stays (0,-6) because x is 0. So the final point is (0, - 6)? Wait, no, maybe the original point is (0,6). Let's re - check.

Wait, the graph: the y - axis is the vertical line. Point A is at (0,6). Reflect across x - axis: (0,6)→(0, - 6) (since reflecting over x - axis changes the sign of y). Then reflect (0,-6) across y - axis: reflecting over y - axis changes the sign of x. So x was 0, so - x is 0. So the point is (0, - 6). Wait, but that seems like the same as after x - axis reflection. But maybe I made a mistake. Wait, no, let's recall the reflection rules:

• Reflection over x - axis: $(x,y)\to(x, - y)$
• Reflection over y - axis: $(x,y)\to(-x,y)$

So starting with A(0,6):

1. Reflect over x - axis: $(0,6)\to(0, - 6)$
2. Reflect over y - axis: $(0,-6)\to(0,-6)$ (because $-x = 0$ when $x = 0$)

So the final point is (0, - 6). But let's check again. Wait, maybe the original point is not (0,6)? Wait, the graph shows A on the y - axis, at y = 6, so x = 0, y = 6. So yes, (0,6). Then x - axis reflection: (0, - 6). Then y - axis reflection: (0, - 6). So the final point is (0, - 6).

Answer:

The final point is (0, - 6), so we plot the point with coordinates (0, - 6) on the graph.