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)

Short 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.

Step-by-step solution

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.