Question

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eflections
trapezoid abcd in the line y = x

1. determine the coordinates of

m(1,-3) after a reflection in the
line x = 2.

1. determine the coordinates of

l(-2,4) after a reflection in the
line y = 4.

Explanation:

Step1: Find the distance between the x - coordinate of point M and the line \(x = 2\)

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

Step2: Calculate the x - coordinate of the reflected point

Since the line \(x = 2\) is vertical, the y - coordinate of the reflected point remains the same. The x - coordinate of the reflected point \(M'\) is \(x=2+(2 - 1)=3\). So the coordinates of the reflected point \(M'\) is \((3,-3)\)

Step3: For point \(L(-2,4)\) and line \(y = 4\)

The formula for the distance between a point \((x_0,y_0)\) and the horizontal line \(y = b\) is \(d=\vert y_0 - b\vert\). For point \(L(-2,4)\) and line \(y = 4\), \(d=\vert4 - 4\vert = 0\)

Step4: Determine the coordinates of the reflected point of \(L\)

Since the distance between \(L(-2,4)\) and \(y = 4\) is \(0\), the point \(L\) lies on the line \(y = 4\). So the reflection of \(L(-2,4)\) in the line \(y = 4\) is itself, i.e., \((-2,4)\)

Answer:

For \(M(1,-3)\) reflected in \(x = 2\): \((3,-3)\)
For \(L(-2,4)\) reflected in \(y = 4\): \((-2,4)\)