Question

3.3 classwork - reflections - graded
state the image of the point (1, -5) after a reflection across the line x = 2.

Explanation:

Step1: Calculate the distance from the point to the line

The x - coordinate of the given point is $x_1 = 1$ and the equation of the line is $x = 2$. The distance $d$ between the point's x - coordinate and the line is $d=|2 - 1|=1$.

Step2: Find the x - coordinate of the reflected point

Since we are reflecting across the vertical line $x = 2$, the x - coordinate of the reflected point $x_2$ is $x_2=2+(2 - 1)=3$. The y - coordinate remains the same during a reflection across a vertical line. So the y - coordinate of the reflected point is $y=-5$.

Answer:

$(3,-5)$