Answer to Question #241585 in Geometry for Lili

Question

In the coordinate plane the point x (-4,4) is translated to the point x (0,-1). Under the same translation the points Y (-2,0) and Z (-1,6) are translated to Y and Z, respectively. What are the coordinates of Y and Z?

Answer 1

Find the translation vector

Let the translation vector be $\begin{pmatrix} a \\ b \end{pmatrix}$

$\begin{pmatrix} a\\ b \end{pmatrix}+\begin{pmatrix} -4 \\ 4 \end{pmatrix}=\begin{pmatrix} 0\\ -1 \end{pmatrix}$

$a-4=0, a=4$

$b+4=-1, b=-5$

The translation vector is $\begin{pmatrix} 0 \\ -5 \end{pmatrix}$

find coordinates of Y

$\begin{pmatrix} 0 \\ -5 \end{pmatrix}+\begin{pmatrix} -2 \\ 0 \end{pmatrix}=\begin{pmatrix} -2 \\ -5 \end{pmatrix}$

coordinates of Y is (-2, -5)

Find the coordinates of Z

$\begin{pmatrix} 0 \\ -5 \end{pmatrix}+\begin{pmatrix} -1 \\ 6 \end{pmatrix}=\begin{pmatrix} -1 \\ 1 \end{pmatrix}$

coordinates of Z is (-1, 1)