Question

the point (-2, -5) is the image of a point that was rotated 180° using center (0, 0). what are the coordinates of the original point before the rotation? enter the coordinates as (x, y).

Explanation:

Step1: Recall 180° rotation rule

A point \((x, y)\) rotated 180° about the origin \((0,0)\) has the image \((-x, -y)\). So, to find the original point, we reverse this: if the image is \((x', y')\), the original point \((x, y)\) satisfies \(x' = -x\) and \(y' = -y\), so \(x = -x'\) and \(y = -y'\).

Step2: Apply the rule to the image point

The image point is \((-2, -5)\). So, the original \(x\)-coordinate is \(-(-2) = 2\), and the original \(y\)-coordinate is \(-(-5) = 5\).

Answer:

\((2, 5)\)