Question

plot the point. then plot the point that is symmetric to it with respect to (a) the x - axis; (b) the y - axis; (c) the origin. (-2,1) plot the point (-2,1). (a) plot the point that is symmetric to (-2,1) with respect to the x - axis. (b) plot the point that is symmetric to (-2,1) with respect to the y - axis.

Explanation:

Step1: Recall x - axis symmetry rule

For a point $(x,y)$ symmetric to the x - axis, the new point is $(x, - y)$. Given the point $(-2,1)$, when symmetric to the x - axis, we change the sign of the y - coordinate.
$(-2,-1)$

Step2: Recall y - axis symmetry rule

For a point $(x,y)$ symmetric to the y - axis, the new point is $(-x,y)$. Given the point $(-2,1)$, when symmetric to the y - axis, we change the sign of the x - coordinate.
$(2,1)$

Step3: Recall origin symmetry rule

For a point $(x,y)$ symmetric to the origin, the new point is $(-x,-y)$. Given the point $(-2,1)$, when symmetric to the origin, we change the signs of both x and y coordinates.
$(2,-1)$

Answer:

(a) $(-2,-1)$
(b) $(2,1)$
(c) $(2,-1)$