Question

question 9 (multiple choice worth 1 points) (02.309 lc) parallelogram abcd is rotated 90° counterclockwise. what rule shows the input and output of the rotation, and what is the new coordinate of a? (x, y)→(-x, -y), a is at (5, -1) (x, y)→(-y, x), a is at (-1, -5) (x, y)→(y, -x), a is at (1, 5) (x, y)→(x, -y), a is at (-5, -1)

Explanation:

Step1: Recall rotation rule

The rule for a 90 - degree counter - clockwise rotation about the origin is $(x,y)\to(-y,x)$.

Step2: Identify original coordinates of A

Assume the original coordinates of point A are $(5,1)$.

Step3: Apply the rotation rule

Using the rule $(x,y)\to(-y,x)$ for point A$(5,1)$, we substitute $x = 5$ and $y = 1$. So, $x'=-y=- 1$ and $y'=x = 5$. The new coordinates of A' are $(-1,5)$.

Answer:

$(x,y)\to(-y,x),A'\text{ is at }(-1,5)$