Question

describe a sequence of transformations that uses the line segments already shown on the coordinate plane to complete a rectangle with the other vertex at (4,0). reflect the line segment with endpoints (-1,2) and (4,2) across the line y =. then, translate the line segment with endpoints (-1,0) and (-1,2) right units. enter the answer in each space provided. use numbers instead of words.

Explanation:

Step1: Reflect the line - segment

The rule for reflecting a point $(x,y)$ across the line $y = 0$ (the $x$ - axis) is $(x,-y)$.
For the point $(-1,2)$, its reflection is $(-1, - 2)$. For the point $(4,2)$, its reflection is $(4,-2)$.

Step2: Translate the line - segment

We want to get from the reflected points to form a rectangle with a vertex at $(4,0)$.
The $x$ - coordinate of the first reflected point $(-1,-2)$ needs to move $4-(-1)=5$ units to the right. The $x$ - coordinate of the second reflected point $(4,-2)$ also needs to move $4 - 4=0$ units to the right.
We translate the reflected line - segment with endpoints $(-1,-2)$ and $(4,-2)$ right 5 units.

Answer:

5; 5