Question

question 10 5 pts which rule describes a rotation of 270 degrees counterclockwise about the origin for any point (x,y)? (x,y)→(y, - x) (x,y)→(x, - y) (x,y)→(-y,x) (x,y)→(-x, - y) a triangle has vertices at (1,1), (4,1), and (1,5). if the triangle is rotated 180 degrees about the origin, what are the coordinates of the image of the vertex (4,1)? (-1, - 4) (4, - 1) (1,4) (-4, - 1)

Explanation:

Step1: Recall rotation rule for 270 - degree counter - clockwise rotation

The rule for a 270 - degree counter - clockwise rotation about the origin for a point $(x,y)$ is $(x,y)\to(y, - x)$.

Step2: Recall rotation rule for 180 - degree rotation

The rule for a 180 - degree rotation about the origin for a point $(x,y)$ is $(x,y)\to(-x,-y)$. Given the point $(4,1)$, when rotated 180 degrees about the origin, we change the sign of both coordinates. So, $x = 4$ becomes $-4$ and $y = 1$ becomes $-1$. The new point is $(-4,-1)$.

Answer:

For the first question: $(x,y)\to(y, - x)$
For the second question: $(-4,-1)$