Math Problem Statement

Point DD is located at left parenthesis, minus, 3, comma, minus, 6, right parenthesis(−3,−6) on the coordinate plane. Point DD is reflected over the xx-axis to create point D, primeD′. Point D, primeD′ is then reflected over the yy-axis to create point D, start superscript, prime, prime, end superscriptD′′. What ordered pair describes the location of D, start superscript, prime, prime, end superscript, question markD′′?

Solution

To solve this, we will follow the reflection steps carefully.

Step 1: Reflect point D(3,6)D(-3, -6) over the x-axis

When reflecting a point over the x-axis, we change the sign of the yy-coordinate, while the xx-coordinate remains unchanged. So:

D(3,6)(3,6)D'(-3, -6) \rightarrow (-3, 6)

Now, point DD' is at (3,6)(-3, 6).

Step 2: Reflect point D(3,6)D'(-3, 6) over the y-axis

When reflecting a point over the y-axis, we change the sign of the xx-coordinate, while the yy-coordinate remains unchanged. So:

D(3,6)(3,6)D'(-3, 6) \rightarrow (3, 6)

Thus, the coordinates of DD'' (point DD reflected over both axes) are (3,6)(3, 6).

Final Answer:

The ordered pair that describes the location of DD'' is (3,6)(3, 6).


Would you like further clarification on any step? Here are 5 related questions to expand your understanding:

  1. How do you reflect a point over the y-axis?
  2. What happens if you reflect a point over both axes simultaneously?
  3. How do you reflect a point over the origin?
  4. What are the general rules for reflections in the coordinate plane?
  5. Can a point's location remain the same after a reflection?

Tip: Reflections in the coordinate plane follow simple rules: over the x-axis, you negate the yy-coordinate, and over the y-axis, you negate the xx-coordinate.

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Math Problem Analysis

Mathematical Concepts

Coordinate Geometry
Reflections in the Coordinate Plane

Formulas

Reflection over x-axis: (x, y) -> (x, -y)
Reflection over y-axis: (x, y) -> (-x, y)

Theorems

Reflection Theorem

Suitable Grade Level

Grades 6-8