Question

the figure below has a point marked with a large dot. first, rotate the figure 270° clockwise about the origin. then, give the coordinates of the marked point in the original figure and the final figure. point in original figure: ( , ) point in final figure: ( , )

Explanation:

Step1: Find the original coordinates

We look at the point in the original figure. The \(x -\)coordinate is \(-4\) and the \(y -\)coordinate is \(-4\). So the original point is \((-4,-4)\).

Step2: Use the rotation rule

The rule for a \(270^{\circ}\) clockwise rotation about the origin \((x,y)\to(y, - x)\).
Substitute \(x=-4\) and \(y = - 4\) into the rule:
When \(x=-4\) and \(y=-4\), the new \(x\) - coordinate is \(y=-4\) and the new \(y\) - coordinate is \(-x=-(-4) = 4\).

Answer:

Point in original figure: \((-4,-4)\)
Point in final figure: \((-4,4)\)