Question

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

Explanation:

Step1: Calculate the distance from point to line

The distance between the x - coordinate of the point $(1,-5)$ (which is $x = 1$) and the line $x = 2$ is $d=|2 - 1|=1$.

Step2: Find the new x - coordinate

To find the x - coordinate of the reflected point, we move the same distance on the other side of the line $x = 2$. So the new x - coordinate is $2+(2 - 1)=3$.

Step3: Determine the y - coordinate

The y - coordinate of a point does not change when reflecting across a vertical line. So the y - coordinate of the reflected point is the same as that of the original point, which is $y=-5$.

Answer:

$(3,-5)$