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Find the point that is symmetric to the point with respect to the -axis, the -axis, and the
origin.
The point symmetric to with respect to the x-axis is
(Type an ordered pair.)

Ask by Kirk Pena. in the United States
Jan 25,2025

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The symmetric point with respect to the -axis is (7, 4).

Solución

To find the point symmetric to with respect to the -axis, you need to reflect the point over the -axis.
Reflection over the -axis:
  • To reflect a point over the -axis, you keep the -coordinate the same and change the sign of the -coordinate.
Given the point :
  • The -coordinate remains .
  • The -coordinate changes from to .
So, the symmetric point with respect to the -axis is:
Answer: (7, 4)

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Mind Expander

The point symmetric to with respect to the -axis is . This is achieved by taking the original point’s -coordinate and changing its sign while keeping the -coordinate the same.
Now, for the -axis reflection, the point would be , flipping the sign of the -coordinate. Finally, the reflection through the origin gives us , changing the signs of both coordinates.

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