Question

the figure below has a point marked with a large dot. first, rotate the figure 270° counterclockwise 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: Identify original coordinates

From the graph, the marked point in the original figure is at \((-4, 6)\) (assuming each grid is 1 unit, moving 4 left on x - axis and 6 up on y - axis).

Step2: Apply 270° counterclockwise rotation rule

The rule for rotating a point \((x,y)\) 270° counterclockwise about the origin is \((x,y)\to(y, - x)\).

Step3: Calculate final coordinates

For the point \((-4,6)\), applying the rule: \(x=-4\), \(y = 6\). So the new \(x\) - coordinate is \(y = 6\) and the new \(y\) - coordinate is \(-x=-(-4)=4\). So the final coordinates are \((6,4)\).

Answer:

Point in original figure: \((-4, 6)\)
Point in final figure: \((6, 4)\)