Question

question 8 5 pts what is the image of the point (2,3) after a rotation of 90 degrees counterclockwise about the origin? (2,-3) (-3,2) (3,-2) (-2,-3) which transformation is equivalent to reflecting a point over the line y = x? switching the x - and y - coordinates: (a,b)→(b,a) negating the y - coordinate: (a,b)→(a,-b) negating both coordinates: (a,b)→(-a,-b) negating the x - coordinate: (a,b)→(-a,b)

Explanation:

Step1: Recall rotation rule

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

Step2: Apply the rule

For the point $(2,3)$, substituting $x = 2$ and $y = 3$ into the rule, we get $(-3,2)$.

The reflection of a point $(a,b)$ over the line $y = x$ swaps the $x$ and $y$ coordinates. That is, the transformation is $(a,b)\to(b,a)$.

Answer:

(-3,2)