Question

question
what is the image of the point $(-7, 5)$ after a rotation of $180^{circ}$ counterclockwise about the origin?

answer attempt 1 out of 2

Explanation:

Step1: Recall the rotation rule

When a point \((x,y)\) is rotated \(180^{\circ}\) counter - clockwise about the origin, the new coordinates \((x',y')\) are given by the rule \((x',y')=(-x,-y)\).

Step2: Apply the rule to the given point

For the point \((-7,5)\), where \(x = - 7\) and \(y = 5\).
Using the formula \((x',y')=(-x,-y)\), we substitute \(x=-7\) and \(y = 5\) into it.
\(x'=-(-7)=7\) and \(y'=-5\).

Answer:

\((7,-5)\)