Question

activator: reflecting points use the coordinate plane to answer each question. a. point f is a reflection of point a across the y-axis. what are the coordinates for point f? (4,2) b. point g is a reflection of point a across the x-axis. what are the coordinates for point g? (-4,-2) c. point h is a reflection of point a across both the x-axis and the y-axis. what are the coordinates for point h?

Explanation:

Part a

Step1: Find coordinates of A

From the graph, point A is at $(-4, 2)$.

Step2: Reflect over y - axis

When reflecting a point $(x,y)$ over the y - axis, the rule is $(x,y)\to(-x,y)$. So for $A(-4,2)$, reflecting over y - axis gives $F(4,2)$.

Step1: Recall coordinates of A

Point A is $(-4, 2)$.

Step2: Reflect over x - axis

The rule for reflecting a point $(x,y)$ over the x - axis is $(x,y)\to(x, -y)$. So for $A(-4,2)$, reflecting over x - axis gives $G(-4,-2)$.

Step1: Recall coordinates of A

Point A is $(-4, 2)$.

Step2: Reflect over both axes

First, reflect over y - axis: $(-4,2)\to(4,2)$ (using $y$ - axis reflection rule). Then reflect the result over x - axis: $(4,2)\to(4,-2)$ (using $x$ - axis reflection rule). Or we can use the rule for reflecting over both axes: $(x,y)\to(-x,-y)$. For $A(-4,2)$, $-x = 4$ and $-y=-2$, so $H(4,-2)$.

Answer:

$(4, 2)$

Part b