Q. 31 - 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 (0, -3)

Step-by-Step Solution

Answer

(a).  (0,3 ) is the point symmetric to (0,-3) in the x-axis  

(b). (0,-3) is the point symmetric to (0,-3) in the y-axis. 

(c).  (0,3) is the point symmetric to (0,-3) in the origin. 

Part (a). Step 1. Given Data

Point  (0,-3) 

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, (0,3 ) is the point symmetric to (0,-3) in the x-axis. 

The two point are shown in the graph below. 

Part (b). Step 1. Given Data

Point (0,-3)

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, (0,-3) is the point symmetric to (0,-3) in the y-axis.

The two point are shown in the graph below

Part (c). Step 1. Given Data

Point (0,-3)

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, (0,3) is the point symmetric to (0,-3) in the origin.

The two point are shown in the graph belo