Math Problem Statement
Point AA is located at left parenthesis, minus, 3, comma, 5, right parenthesis(−3,5) on the coordinate plane. Point AA is reflected over the yy-axis to create point A, primeA ′ . Point A, primeA ′ is then reflected over the xx-axis to create point A, start superscript, prime, prime, end superscriptA ′′ . What ordered pair describes the location of A, start superscript, prime, prime, end superscript, question markA ′′ ?
Solution
Let's solve the problem step by step, reflecting point over the axes to find the final location.
1. Reflecting Point over the y-axis:
When reflecting over the y-axis, the x-coordinate changes its sign while the y-coordinate remains the same. The coordinates of will be:
2. Reflecting Point over the x-axis:
When reflecting over the x-axis, the y-coordinate changes its sign while the x-coordinate remains the same. The coordinates of will be:
Final Answer:
The ordered pair that describes the location of is .
Do you want any more details on the reflection process or have further questions?
Here are five related questions:
- How would the coordinates change if were reflected over the x-axis first, then the y-axis?
- What is the general rule for reflecting a point over both the x- and y-axes?
- Can you reflect a point over a diagonal line, like ?
- How do reflections affect the distances between points on the coordinate plane?
- What happens when you reflect a point twice over the same axis?
Tip: When reflecting a point, always check which axis you're reflecting over and remember how each coordinate changes!
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Geometry
Coordinate Geometry
Reflections
Formulas
Reflection over the y-axis: (x, y) -> (-x, y)
Reflection over the x-axis: (x, y) -> (x, -y)
Theorems
Reflection Theorem: Reflecting a point across the y-axis negates the x-coordinate.
Reflection Theorem: Reflecting a point across the x-axis negates the y-coordinate.
Suitable Grade Level
Grades 6-8