Q. 25 - 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 (-2, 1)

Step-by-Step Solution

Answer

(a).  (-2,-1) is the point symmetric to (-2 ,1 ) in the x-axis.

(b).   (2 ,1 ) is the point symmetric to (-2,1 ) in the y-axis.

(c).  (2,-1 ) is the point symmetric to (-2,1 ) in the origin.

Part (a). Step 1. Given Data

( -2,1 )

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, ( -2 ,1 ) is the point symmetric to (-2 ,-1 ) in the x-axis.

Part (b). Step 1. Given Data

Point (-2,1)

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, (-2,1 ) is the point symmetric to (2,1 ) in the x-axis.

Part (c). Step 1. Given Data

Point ( -2,1 ) 

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, (-2.1) is the point symmetric to (2,-1) in the origin.