Question

1. why do we need to add 2 to the x and add 1 to the y? the video said to. the center of rotation is supposed to be at the point (2, 1) we altered the original point by subtracting 2 and subtracting 1. then add 2 and add 1 cancels out what was done previously to alter the points. we dont need to add 2 to the x and add 1 to the y.

Explanation:

When rotating a point \((x,y)\) around a center of rotation \((a,b)\), we first translate the point so that the center of rotation is at the origin. This is done by subtracting \(a\) from \(x\) and \(b\) from \(y\). After performing the rotation (in this case, a \(90^{\circ}\) rotation), we then translate the point back by adding \(a\) to the \(x\)-coordinate and \(b\) to the \(y\)-coordinate. Here, \(a = 2\) and \(b=1\). So, we first subtract \(2\) from \(x\) and \(1\) from \(y\) (to recenter around the origin for rotation), and then after rotation, we add \(2\) to \(x\) and \(1\) to \(y\) (to recenter back to the original center of rotation \((2,1)\)).

Answer:

B. The center of rotation is supposed to be at the point \((2,1)\)
C. We altered the original point by subtracting \(2\) and subtracting \(1\). Then add \(2\) and add \(1\) cancels out what was done previously to alter the points.