Questions: 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. (5,4)

Transcript text: 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. \[ (5,4) \]

Solution

Solution Steps

Step 1: Symmetry with respect to the $x$-axis

The symmetric point with respect to the $x$-axis will have the same $x$-coordinate and the opposite $y$-coordinate. Thus, if the original point is $(x, y) = (5, 4)$, the symmetric point will be $(x, -y) = (5, -4)$.

Step 2: Symmetry with respect to the $y$-axis

The symmetric point with respect to the $y$-axis will have the opposite $x$-coordinate and the same $y$-coordinate. Thus, if the original point is $(x, y) = (5, 4)$, the symmetric point will be $(-x, y) = (-5, 4)$.

Step 3: Symmetry with respect to the origin

The symmetric point with respect to the origin will have both coordinates opposite to the original point. Thus, if the original point is $(x, y) = (5, 4)$, the symmetric point will be $(-x, -y) = (-5, -4)$.