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 AA over the axes to find the final location.

1. Reflecting Point A(3,5)A(-3, 5) 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 AA' will be:

A=(3,5)A' = (3, 5)

2. Reflecting Point A(3,5)A'(3, 5) 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 AA'' will be:

A=(3,5)A'' = (3, -5)

Final Answer:

The ordered pair that describes the location of AA'' is (3,5)(3, -5).


Do you want any more details on the reflection process or have further questions?

Here are five related questions:

  1. How would the coordinates change if AA were reflected over the x-axis first, then the y-axis?
  2. What is the general rule for reflecting a point over both the x- and y-axes?
  3. Can you reflect a point over a diagonal line, like y=xy = x?
  4. How do reflections affect the distances between points on the coordinate plane?
  5. 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!

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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