Question

point a is graphed at (-4, 4). using the pencil, plot the image of point a after a 180° clockwise rotation about (-2, -1).

Explanation:

Step1: Recall rotation formula

To rotate a point \((x,y)\) 180° about a center \((h,k)\), we use the formula: \((x', y') = (2h - x, 2k - y)\). Here, the original point \(A\) is \((-4, 4)\) and the center of rotation \((h,k)\) is \((-2, -1)\).

Step2: Calculate new x - coordinate

Substitute \(x = -4\), \(h = -2\) into the formula for \(x'\):
\(x' = 2\times(-2)-(-4)= -4 + 4 = 0\)

Step3: Calculate new y - coordinate

Substitute \(y = 4\), \(k = -1\) into the formula for \(y'\):
\(y' = 2\times(-1)-4 = -2 - 4 = -6\)

Answer:

The image of point \(A\) after a 180° clockwise rotation about \((-2, -1)\) is \((0, -6)\).