Questions: If triangle XYZ is reflected across the line y=1 to create triangle X'Y'Z', what is the ordered pair of x?

Transcript text: If triangle $X Y Z$ is reflected across the line $y=1$ to create triangle $X^{\prime} Y^{\prime} Z^{\prime}$, what is the ordered pair of $\times$?

Solution

Solution Steps

Step 1: Identify the coordinates of point X

The coordinates of point X are given as (3, -2).

Step 2: Determine the line of reflection

The line of reflection is $ y = 1 $.

Step 3: Calculate the reflected coordinates

To reflect a point across the line $ y = 1 $, we use the formula: \[ y' = 2 \cdot 1 - y \] For point X (3, -2): \[ y' = 2 \cdot 1 - (-2) = 2 + 2 = 4 \] Thus, the reflected coordinates of point X are (3, 4).

Final Answer

The ordered pair of $ X' $ is (3, 4).

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