Question

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

Explanation:

Step1: Calculate the distance from the point to the line

The distance between the y - coordinate of the point $(-2,-1)$ (which is $y_1=-1$) and the line $y = 1$ is $d=|1-(-1)|=2$.

Step2: Find the new y - coordinate

When reflecting a point across the line $y = 1$, the x - coordinate remains the same. The new y - coordinate is $y_2=1 + 2=3$ since we move the same distance on the other side of the line $y = 1$. The x - coordinate of the point $(-2,-1)$ stays $x=-2$.

Answer:

$(-2,3)$