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).

Explanation:

Step1: Symmetry about x - axis

When a point $(x,y)$ is symmetric about the x - axis, the x - coordinate remains the same and the y - coordinate changes its sign. Given the point $(-2,1)$, for symmetry about the x - axis, the new point is $(-2,-1)$.

Step2: Symmetry about y - axis

When a point $(x,y)$ is symmetric about the y - axis, the y - coordinate remains the same and the x - coordinate changes its sign. For the point $(-2,1)$, the symmetric point about the y - axis is $(2,1)$.

Step3: Symmetry about the origin

When a point $(x,y)$ is symmetric about the origin, both the x - coordinate and the y - coordinate change their signs. For the point $(-2,1)$, the symmetric point about the origin is $(2,-1)$.

Answer:

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