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 (-1, -1)

Short answer

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

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

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

Step-by-step solution

Part (a).  Step 1.  Given Data 

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

The two point are shown in the graph below

Part (b).  Step 1.  Given Data  

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

The two point are shown in the graph below

Part (c).  Step 1.  Given Data   

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

The two point are shown in the graph below