Question

4.1 engage: grid transformations
due on 10.30.2025 10 total points 2 total attempts
answer the question correctly to continue:
what is the image of the point $(3, - 4)$ after a $180^{circ}$ rotation about the origin?
$(-4, -3)$ $(-3,4)$
$(4, -3)$ $(3,4)$

Explanation:

Step1: Recall the rotation rule

When a point \((x,y)\) is rotated \(180^{\circ}\) 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 \((3, - 4)\), where \(x = 3\) and \(y=-4\).
Substitute \(x = 3\) and \(y =-4\) into \((-x,-y)\).
We get \((-3,4)\).

Answer:

\((-3,4)\)