Math Problem Statement
Solution
The image shows two shapes, A and B, reflected across a line on the coordinate plane. To find the equation of the line across which shape A is reflected to form shape B, we need to determine which line creates this reflection.
Looking at the graph:
- Shape A is located below the x-axis, while shape B is located above the x-axis.
- The reflection appears to be over the x-axis, as the relative positioning of the two shapes suggests a vertical flip.
Thus, the line of reflection is the x-axis, which has the equation:
The completed sentence would be:
"Shape B is a reflection of shape A in the line with equation y = 0."
Would you like any further details or clarification?
5 Related Questions:
- What is the general formula for reflecting a point over the x-axis?
- How would the reflection change if it were over the y-axis instead?
- Can you explain how to reflect a shape over any arbitrary line?
- What is the process for determining the line of reflection between two shapes?
- How would a reflection differ from a rotation or translation?
Tip:
When reflecting a shape across a line, the line of reflection acts like a mirror, meaning every point on the shape has a corresponding point on the reflected shape, equidistant from the mirror line.
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Math Problem Analysis
Mathematical Concepts
Reflection
Coordinate Geometry
Formulas
Equation of a line: y = mx + c
Reflection over the x-axis
Theorems
Line of reflection acts as a perpendicular bisector between corresponding points
Suitable Grade Level
Grades 7-9