Question

s and r are points on a polygon. s and r are the points under a translation. find r.
s(-3, -4)
s(-6, 9)
r(10, 2)
show your work here

Explanation:

Step1: Find the translation vector

To find the translation vector, we subtract the coordinates of \( S \) from \( S' \). Let the translation vector be \( (h, k) \), where \( h = x_{S'} - x_S \) and \( k = y_{S'} - y_S \).
For \( x \)-coordinate: \( h = -6 - (-3) = -6 + 3 = -3 \)
For \( y \)-coordinate: \( k = 9 - (-4) = 9 + 4 = 13 \)
So the translation vector is \( (-3, 13) \).

Step2: Apply the translation to \( R \)

To find \( R' \), we add the translation vector \( (-3, 13) \) to the coordinates of \( R(10, 2) \).
For \( x \)-coordinate of \( R' \): \( x_{R'} = 10 + (-3) = 7 \)
For \( y \)-coordinate of \( R' \): \( y_{R'} = 2 + 13 = 15 \)

Answer:

\( R' \) is \( (7, 15) \)