Use the image to answer the question.

Question

An illustration shows a coordinate plane. Both x- and y-axes range from negative 10 to 10 in one unit increments. A quadrilateral with vertices P Q R S is drawn on it. Vertex P is at coordinates left parenthesis 4 comma 6 right parenthesis, vertex Q is at coordinates left parenthesis 7 comma 2 right parenthesis, vertex R is at coordinates left parenthesis 5 comma negative 2 right parenthesis, and vertex S is at coordinates left parenthesis 2 comma 2 right parenthesis.

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

(1 point)
(
)

Answer 1

To find the coordinates of point \( S' \) after translating point \( S(2, 2) \) six units up and four units to the left, we need to adjust the y-coordinate and the x-coordinate accordingly.

• Translating 6 units up means we add 6 to the y-coordinate: \[ y' = 2 + 6 = 8 \]

• Translating 4 units to the left means we subtract 4 from the x-coordinate: \[ x' = 2 - 4 = -2 \]

So, the new coordinates of point \( S' \) are: \[ S' = (-2, 8) \]