8. Points $R, S$, and $T$ have the coordinates $R(5,-9), S(15,3)$, and $T(3,-8)$. Together the points make a triangle. If the triangle was translated so that point $R$ ended up at the coordinates $(8,12)$ what would be the new coordinates of point $S$ ? $(9,25)$ $(13,15)$ $(18,24)$ $(19,19)$
Solution
Step 1 ：Given the coordinates of points R and S as R(5,-9) and S(15,3) respectively.
Step 2 ：Point R is translated to a new position (8,12).
Step 3 ：We need to find the new coordinates of point S after the same translation.
Step 4 ：The change in the x-coordinate from the original position of R to the new position is calculated as \(8 - 5 = 3\).
Step 5 ：The change in the y-coordinate from the original position of R to the new position is calculated as \(12 - (-9) = 21\).
Step 6 ：We apply the same changes to the coordinates of point S.
Step 7 ：The new x-coordinate of point S is calculated as \(15 + 3 = 18\).
Step 8 ：The new y-coordinate of point S is calculated as \(3 + 21 = 24\).
Step 9 ：So, the new coordinates of point S after the translation are \(\boxed{(18, 24)}\).
