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Graph the Image of Triangle RST After Reflection Over the x-axis
Mathematics
Grade 8 (Junior High)
Question Content
Graph the image of \( \triangle RST \) after a reflection over the \( x \)-axis. The vertices of \( \triangle RST \) are \( R(-4, -10) \), \( S(0, -10) \), and \( T(0, -4) \) (derived from the grid).
Correct Answer
The reflected triangle \( \triangle R'S'T' \) has vertices \( R'(-4, 10) \), \( S'(0, 10) \), and \( T'(0, 4) \). Plot these points and connect them to form the image.
Detailed Solution Steps
1
1. Identify the coordinates of the original vertices: \( R(-4, -10) \), \( S(0, -10) \), \( T(0, -4) \).
2
2. Apply the reflection rule over the \( x \)-axis: For any point \( (x, y) \), the reflection is \( (x, -y) \).
3
3. Calculate the reflected coordinates:
4
- \( R(-4, -10) \rightarrow R'(-4, 10) \) (since \( -(-10) = 10 \)),
5
- \( S(0, -10) \rightarrow S'(0, 10) \) (since \( -(-10) = 10 \)),
6
- \( T(0, -4) \rightarrow T'(0, 4) \) (since \( -(-4) = 4 \)).
7
4. Plot the reflected points \( R' \), \( S' \), and \( T' \) on the grid and connect them to form the reflected triangle.
Knowledge Points Involved
1
Reflection over the x-axis
The transformation rule for reflecting a point \( (x, y) \) over the \( x \)-axis is \( (x, y) \rightarrow (x, -y) \). This flips the point across the \( x \)-axis, reversing the sign of the \( y \)-coordinate.
2
Coordinate Geometry (Grid Coordinates)
Identifying the \( x \)- and \( y \)-coordinates of points on a Cartesian grid, where the \( x \)-coordinate represents horizontal position and the \( y \)-coordinate represents vertical position.
3
Graphing Transformed Figures
Plotting the transformed vertices (after applying a geometric transformation like reflection) and connecting them to visualize the image of the original figure.
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