Question
Find the point that is symmetric to the point \( (7,-4) \) with respect to the \( x \)-axis, the \( y \)-axis, and the origin. The point symmetric to \( (7,-4) \) with respect to the x-axis is (Type an ordered pair.)
Ask by Kirk Pena. in the United States
Jan 25,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The symmetric point with respect to the \( x \)-axis is (7, 4).
Solution
To find the point symmetric to \( (7, -4) \) with respect to the \( x \)-axis, you need to reflect the point over the \( x \)-axis.
**Reflection over the \( x \)-axis:**
- To reflect a point over the \( x \)-axis, you keep the \( x \)-coordinate the same and change the sign of the \( y \)-coordinate.
Given the point \( (7, -4) \):
- The \( x \)-coordinate remains \( 7 \).
- The \( y \)-coordinate changes from \(-4\) to \(4\).
So, the symmetric point with respect to the \( x \)-axis is:
\[
(7, 4)
\]
**Answer:** (7, 4)
Reviewed and approved by the UpStudy tutoring team
Like
error msg
Explain 
Simplify this solution Mind Expander
The point symmetric to \( (7,-4) \) with respect to the \( x \)-axis is \( (7, 4) \). This is achieved by taking the original point's \( y \)-coordinate and changing its sign while keeping the \( x \)-coordinate the same. Now, for the \( y \)-axis reflection, the point would be \( (-7,-4) \), flipping the sign of the \( x \)-coordinate. Finally, the reflection through the origin gives us \( (-7, 4) \), changing the signs of both coordinates.
