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.

Answer 1

(a) Symmetric to the x - axis: ( 7, 8)

(b) Symmetric to the y - axis: (-7, -8)

(c) Symmetric to the origin: (-7, 8)

Step-by-step explanation:

(a)

A point (a,b) is said to be symmetric with respect to the x-axis when

`(a,b)\to(-a,b)`

therefore, for the point ( 7, -8) a point that is symmetric with respect to the x-axis is

`(7,-8)\to(7,8)`

Hence, a point symmetric to (7, -8) with respect to the x-axis is (7,8).

(b)

A point (a,b) is said to be symmetric with respect to the y-axis when

`(a,b)\to(-a,b)`

therefore, for the point ( 7, -8) a point that is symmetric with respect to the y-axis is

`(7,-8)\to(-7,-8)`

Hence, a point symmetric to (7, -8) with respect to the y-axis is (-7,-8).

(c).

A point (a,b) is said to be symmetric with respect to the origin when

`(a,b)\to(-a,-b)`

therefore, for the point (7, -8), a point symmetric with respect to the origin is

`(7,-8)\to(-7,8)`

Hence, a point symmetric to (7, -8) with respect to the origin is (-7,8).

The graph of the three points is given below: