Question

the coordinates of point b are (3, 4). determine the coordinates of b after a reflection in the line y = 1. * (10 points) (-3, -2) (3, -2) (3, 2) (-3, 2)

Explanation:

Step1: Analyze the reflection rule for the y - coordinate

When reflecting a point \((x,y)\) over the line \(y = a\), the formula for the new \(y\) - coordinate is \(y'=2a - y\), and the \(x\) - coordinate remains the same (\(x'=x\)). Here \(a = 1\) and the original point is \(B(3,4)\).

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

Substitute \(x = 3\), \(y = 4\), and \(a = 1\) into the formula.
For the \(x\) - coordinate: \(x'=3\) (since there is no change in the \(x\) - direction when reflecting over a horizontal line \(y = 1\)).
For the \(y\) - coordinate: \(y'=2\times1-4=2 - 4=-2\).

Answer:

\((3,-2)\) (the second option)