P = (4, 6)

Question

S = (2, 2)
R = (5, -2)
Q = (7, 2)

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

Answer 1

To find the coordinates of point \( S' \) after translating point \( S \) (which is at \( (2, 2) \)) 6 units up and 4 units to the left, we can apply the following transformations:

1. Translation 6 units up: This means we add 6 to the y-coordinate. \[ y' = 2 + 6 = 8 \]

2. Translation 4 units to the left: This means we subtract 4 from the x-coordinate. \[ x' = 2 - 4 = -2 \]

Thus, the new coordinates for point \( S' \) after the translation will be: \[ S' = (-2, 8) \]