Question

P=4,6
Q=7,2
R=5,-2
S=2,2
If figure PQRS
is translated 6 units up and 4 units to the left, what are the coordinates of point S′
?

Answer 1

To determine the new coordinates of point \( S' \) after a translation of 6 units up and 4 units to the left, we start with the original coordinates of point \( S \):

\[
S = (2, 2)
\]

### Step 1: Translate 4 units to the left.
When translating to the left, we subtract from the x-coordinate:

\[
x' = 2 - 4 = -2
\]

### Step 2: Translate 6 units up.
When translating up, we add to the y-coordinate:

\[
y' = 2 + 6 = 8
\]

### Final Coordinates
Combining these transformations, the new coordinates for point \( S' \) will be:

\[
S' = (-2, 8)
\]

Thus, the coordinates of point \( S' \) after the translation are \((-2, 8)\).