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.

Translate figure PQRS
6 units down and 2 units to the right. What are the coordinates of P′
?

(1 point)
Responses

(6, 0)
left parenthesis 6 comma 0 right parenthesis

(2, 12)
left parenthesis 2 comma 12 right parenthesis

(10, 4)
left parenthesis 10 comma 4 right parenthesis

(2, 0)

Answer 1

To translate the point \( P(4, 6) \) 6 units down and 2 units to the right, we perform the following calculations:

1. Translation Down: To move down by 6 units, we subtract 6 from the y-coordinate: \[ 6 - 6 = 0 \]

2. Translation Right: To move right by 2 units, we add 2 to the x-coordinate: \[ 4 + 2 = 6 \]

So, the new coordinates of \( P' \) after the translation are \( (6, 0) \).

The correct response is: \[ (6, 0) \]