Question

1. a line of reflection is represented by the equation y = -2. what is the reflection of the point (5, -1)? (5, 1) (5, -5) (5, -3) (5, 3)

Explanation:

Step1: Calculate the distance between the y - coordinate of the point and the line of reflection

The line of reflection is \(y = - 2\), and the y - coordinate of the point \((5,-1)\) is \(y_1=-1\). The distance \(d\) between \(y = - 1\) and \(y=-2\) is \(d=\vert-1-(-2)\vert=\vert-1 + 2\vert = 1\).

Step2: Find the y - coordinate of the reflected point

Since we are reflecting over the line \(y=-2\), for a point \((x,y)\) reflected over the horizontal line \(y = k\), the formula for the y - coordinate of the reflected point \((x,y')\) is \(y'=2k - y\). Here \(k=-2\) and \(y=-1\), so \(y'=2\times(-2)-(-1)=-4 + 1=-3\). The x - coordinate remains the same because the line of reflection \(y=-2\) is horizontal.

Answer:

\((5,-3)\)