Question

function transformations - reflections
identify and plot the point that is a x - axis reflection of the point in figure 1.
identify and plot the point that is a y - axis reflection of the point in figure 2.
x - axis reflection:
y - axis reflection:
figure 1
figure 2
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Explanation:

Step1: Identify original point (Fig1)

Original point: $(-5, -2)$

Step2: Reflect over x-axis

Rule: $(x,y)\to(x,-y)$
New point: $(-5, -(-2))=(-5, 2)$

Step3: Identify original point (Fig2)

Original point: $(-5, -2)$

Step4: Reflect over y-axis

Rule: $(x,y)\to(-x,y)$
New point: $(-(-5), -2)=(5, -2)$

Answer:

x-axis Reflection: $(-5, 2)$
y-axis Reflection: $(5, -2)$

(To plot: For the x-axis reflection, mark a dot at $(-5, 2)$ on Figure 1. For the y-axis reflection, mark a dot at $(5, -2)$ on Figure 2.)