8. A quadrilateral is translated 5 units right and 3 units down on a coordinate plane. Which expressions could be used to find one of the coordinates of the vertices of the image? Select all that are correct. \( \begin{array}{ll}\text { (A) } x-3 & \text { (D) } y-3 \\ \text { (B) } x-5 & \text { (E) } y+3 \\ \text { (C) } x+5 & \text { (F) } y+5\end{array} \)

To determine the correct expressions for finding one of the coordinates of the vertices of the image after the translation, we need to understand how translation affects the coordinates of a point. When a point \((x, y)\) is translated 5 units to the right, the x-coordinate increases by 5. Therefore, the new x-coordinate will be: \[ x' = x + 5 \] When the point is translated 3 units down, the y-coordinate decreases by 3. Therefore, the new y-coordinate will be: \[ y' = y - 3 \] Now, let's analyze the options provided: - (A) \(x - 3\): This does not represent the new x-coordinate after translation. - (B) \(x - 5\): This does not represent the new x-coordinate after translation. - (C) \(x + 5\): This correctly represents the new x-coordinate after translation. - (D) \(y - 3\): This does not represent the new y-coordinate after translation. - (E) \(y + 3\): This does not represent the new y-coordinate after translation. - (F) \(y + 5\): This does not represent the new y-coordinate after translation. Thus, the correct expression that could be used to find one of the coordinates of the vertices of the image is: **(C) \(x + 5\)** And for the y-coordinate, the correct expression would be: **(D) \(y - 3\)** So the correct answers are **(C)** and **(D)**.