Question

a circle is graphed on a coordinate grid with its center at (11, -8). the circle will be translated u units to the left and l units up. which rule describes the center of the new circle after this translation? (x, y) → (-8 + l, 11 - (x, y) → (11 - u, -8 + l) (x, y) → (11u, -8l) (x, y) → (11 + u, -8 - l)

Explanation:

Step1: Understand horizontal translation

When a point \((x,y)\) is translated \(U\) units to the left, the \(x -\) coordinate changes. The rule for horizontal translation: if we move \(U\) units to the left, the new \(x-\) coordinate is \(x - U\). Here \(x = 11\), so the new \(x-\) coordinate is \(11 - U\).

Step2: Understand vertical translation

When a point \((x,y)\) is translated \(L\) units up, the \(y-\) coordinate changes. The rule for vertical translation: if we move \(L\) units up, the new \(y-\) coordinate is \(y+L\). Here \(y=-8\), so the new \(y-\) coordinate is \(-8 + L\).

Answer:

\((x,y)\to(11 - U,-8 + L)\)