Question

determine the translation that maps a to a. write your answer in the form \langle x, y \
angle.\
a(1, -10)\
a(-3, -11)\
show your work here

Explanation:

Step1: Find the change in x - coordinate

To find the change in the x - coordinate, we subtract the x - coordinate of point A from the x - coordinate of point \(A'\). Let the change in x be \(\Delta x\). The x - coordinate of \(A\) is \(x_A = 1\) and the x - coordinate of \(A'\) is \(x_{A'}= - 3\). So, \(\Delta x=x_{A'}-x_A=-3 - 1=-4\).

Step2: Find the change in y - coordinate

To find the change in the y - coordinate, we subtract the y - coordinate of point A from the y - coordinate of point \(A'\). Let the change in y be \(\Delta y\). The y - coordinate of \(A\) is \(y_A=-10\) and the y - coordinate of \(A'\) is \(y_{A'}=-11\). So, \(\Delta y = y_{A'}-y_A=-11-(-10)=-11 + 10=-1\).

Answer:

\(\langle - 4,-1
angle\)