Questions: What is the line of reflection for the following: y=x x axis y axis y=-x

What is the line of reflection for the following: y=x x axis y axis y=-x
Transcript text: What is the line of reflection for the following: $y=x$ $x$ axis y axis $y=-x$
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Solution

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Solution Steps

Step 1: Identify the Points

Identify the points of the original shape and its reflected image.

  • Original points (Green): (-1, 4), (-2, 2), (-1, 2), (-2, 0)
  • Reflected points (Blue): (1, 4), (2, 2), (1, 2), (2, 0)
Step 2: Determine the Midpoints

Calculate the midpoints between each pair of corresponding points from the original and reflected shapes.

  • Midpoint between (-1, 4) and (1, 4): \((\frac{-1+1}{2}, \frac{4+4}{2}) = (0, 4)\)
  • Midpoint between (-2, 2) and (2, 2): \((\frac{-2+2}{2}, \frac{2+2}{2}) = (0, 2)\)
  • Midpoint between (-1, 2) and (1, 2): \((\frac{-1+1}{2}, \frac{2+2}{2}) = (0, 2)\)
  • Midpoint between (-2, 0) and (2, 0): \((\frac{-2+2}{2}, \frac{0+0}{2}) = (0, 0)\)
Step 3: Identify the Line of Reflection

Observe that all midpoints lie on the y-axis (x = 0).

Final Answer

The line of reflection is the y-axis.

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