Q. 26 - Precalculus Enhanced with Graphing Utilities

Question

Plot each point. Then plot the point that is symmetric to it with respect to -

(a) the x-axis

(b) the y-axis

(c) the origin

Point (4, -2)

Step-by-Step Solution

Answer

(a). (4, 2 ) is the point symmetric to (4,-2) in the x-axis. 

(b). (-4,-2) is the point symmetric to (4,-2) in the y-axis.

(c).  (-4,2) is the point symmetric to (4,-2) in the origin.

Part (a). Step 1. Given Data

Point  ( 4,-2)

Part (a). Step 2. To Find

Plot the point that is symmetric to it with respect to the x-axis 

Part (a). Step 3. Explanation

• (x,-y) is the point symmetric to (x, y) in the x-axis.

• Therefore, (4, 2 ) is the point symmetric to (4,-2) in the x-axis. 

The two point are shown in the graph below.

Part (b). Step 1. Given Data

Point (4,-2) 

Part (b). Step 2. To Find

Plot the point that is symmetric to it with respect to the y-axis 

Part (b). Step 3. Explanation

• (-x, y) is the point symmetric to (x, y) in the y-axis.

Therefore, (-4,-2) is the point symmetric to (4,-2) in the y-axis.

The two point are shown in the graph below

Part (c). Step 1. Given Data

Point (4,-2) 

Part (c). Step 2. To Find

Plot the point that is symmetric to it with respect to the origin. 

Part (c). Step 3. Explanation

• (-x,-y) is the point symmetric to (x, y) in the origin.

• Therefore, (-4,2) is the point symmetric to (4,-2) in the origin.

The two point are shown in the graph below