Question

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reflections

1. trapezoid abcd in the line y = x
2. determine the coordinates of m(1,-3) after a reflection in the line x = 2.
3. determine the coordinates of l(-2,4) after a reflection in the line y = 4.

Explanation:

Step1: Find the distance between the point and the line

The formula for the distance between a point \((x_0,y_0)\) and the line \(x = a\) is \(d=\vert x_0 - a\vert\).
For the point \(M(1,-3)\) and the line \(x = 2\), \(d=\vert1 - 2\vert=1\).

Step2: Calculate the new \(x\) - coordinate

Since the line of reflection is \(x = 2\), and the distance from \(x = 1\) to \(x = 2\) is \(1\). The new \(x\) - coordinate \(x=2+(2 - 1)=3\). The \(y\) - coordinate remains the same.

Answer:

The coordinates of the reflected point are \((3,-3)\)