Q. 23 - 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  (3, 4)

Step-by-Step Solution

Answer

(a).  (3,-4) is the point symmetric to (3,4) in the x-axis.

 

(b).   (-3,4) is the point symmetric to (3,4) in the y-axis.

(c).  (-3,-4) is the point symmetric to (3,4) in the x-axis. 

Part (a). Step 1. Given Data

Point (3,4)

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, (3,-4) is the point symmetric to (3,4) in the x-axis.

The two point are shown in the graph below.

Part (b). Step 1. Given Data

Point (3,4)

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, (-3,4) is the point symmetric to (3,4) in the x-axis.

The two point are shown in the graph below

Part (c). Step 1. Given Data

Point (3,4)

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, (-3,-4) is the point symmetric to (3,4) in the origin.

The two point are shown in the graph below