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 over the x-axis
When reflecting a point over the x-axis, we change the sign of the -coordinate, while the -coordinate remains unchanged. So:
Now, point is at .
Step 2: Reflect point over the y-axis
When reflecting a point over the y-axis, we change the sign of the -coordinate, while the -coordinate remains unchanged. So:
Thus, the coordinates of (point reflected over both axes) are .
Final Answer:
The ordered pair that describes the location of is .
Would you like further clarification on any step? Here are 5 related questions to expand your understanding:
- How do you reflect a point over the y-axis?
- What happens if you reflect a point over both axes simultaneously?
- How do you reflect a point over the origin?
- What are the general rules for reflections in the coordinate plane?
- 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 -coordinate, and over the y-axis, you negate the -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