Question

1. a circle is graphed on a coordinate grid with its center (-3, 6) the circle translated w units to the left, and 7 units up. which rule describes the center of the new circle after this translation?

a. $(x,y) \to (-3 + w, 6 - 7)$
b. $(x,y) \to (6 + 7, - 3 - w)$
c. $(x,y) \to (-3 - w, 6 +7)$
d. $(x,y) \to (6 +7, -3 - w)$
c. $(x,y) \to (x + 2, y - 3)$
d. $(x,y) \to (x - 1, y + 2)$

Explanation:

Step1: Translate left by w units

For an x-coordinate, moving left subtracts w: $x
ightarrow x - w$
Original x-coordinate: $-3$, so new x: $-3 - w$

Step2: Translate up by 7 units

For a y-coordinate, moving up adds 7: $y
ightarrow y + 7$
Original y-coordinate: $6$, so new y: $6 + 7$

Step3: Write coordinate transformation

The rule applies to all points $(x,y)$ on the circle, mapping to the new coordinates.

Answer:

C. $(x,y)
ightarrow (-3 - w, 6 + 7)$