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. (5, - 7) plot the point (5, - 7).

Explanation:

Step1: Recall x - axis symmetry rule

For a point $(x,y)$ symmetric about the x - axis, the new point is $(x, - y)$. Given the point $(5,-7)$, the symmetric point about the x - axis is $(5,7)$.

Step2: Recall y - axis symmetry rule

For a point $(x,y)$ symmetric about the y - axis, the new point is $(-x,y)$. Given the point $(5,-7)$, the symmetric point about the y - axis is $(-5,-7)$.

Step3: Recall origin symmetry rule

For a point $(x,y)$ symmetric about the origin, the new point is $(-x,-y)$. Given the point $(5,-7)$, the symmetric point about the origin is $(-5,7)$.

Answer:

Symmetric to $(5, - 7)$ about:
(a) x - axis: $(5,7)$
(b) y - axis: $(-5,-7)$
(c) origin: $(-5,7)$