Question

problem 3
points f, and g are plotted on the coordinate plane.
plot the coordinates of points f and g after a reflection over
the x - axis.
then enter the coordinates in the table.

point	coordinates
$g$	input box

Explanation:

Step1: Find coordinates of F

From the graph, point F is at (2, -2) (assuming each grid is 1 unit, moving 2 right on x - axis and 2 down on y - axis).

Step2: Reflect F over x - axis

The rule for reflection over the x - axis is \((x,y)\to(x, - y)\). For F(2, - 2), applying the rule: \(x = 2\), \(y=-2\), so \(-y = 2\). Thus, \(F'=(2,2)\).

Step3: Find coordinates of G

From the graph, point G is at (0, 4) (on y - axis, 4 units up).

Step4: Reflect G over x - axis

Using the reflection rule \((x,y)\to(x, - y)\) for G(0, 4), \(x = 0\), \(y = 4\), so \(-y=-4\). Thus, \(G'=(0, - 4)\).

Answer:

For \(F'\): \((2,2)\)
For \(G'\): \((0, - 4)\)