Question

Use arrow notation to write a rule for finding the coordinates of a point P(x,y) after a rotation of 270° about

the origin.
a {x,y) - P'(x2y)
c. P(x,y) → P' *, -»)
Px,y) P'(x,-»)
d. P(x, y) + PU, “x)
I

Answer 1

Explanation:

B

Answer 2

Rotate coordinates 270° counter-clockwise: (x, y) -> (-y, x) and the correct option is D.

Arrow notation is a way to represent geometric transformations using arrows. To represent a rotation of 270° about the origin, we draw an arrow from the original point to the rotated point, and label the arrow with the angle of rotation.

In the case of a 270° rotation about the origin, the arrow will point from the original point to the point that is reflected across the y-axis and then rotated 90° counterclockwise. This means that the new coordinates of the point will be (y,-x).

We can use arrow notation to represent this transformation as follows:

P(x,y) → P'(y,-x)

where P(x,y) is the original point and P'(y,-x) is the rotated point.

Here is an example of how to use arrow notation to find the coordinates of a point after a rotation of 270° about the origin:

Suppose we have the point P(-2,3). To find the coordinates of P' after a rotation of 270° about the origin, we draw an arrow from P to P', and label the arrow with the angle of rotation:

(-2,3) → P'

270°

Since the arrow points to the point that is reflected across the y-axis and then rotated 90° counterclockwise, the coordinates of P' are (3,2).

Therefore, the arrow notation for the rule for finding the coordinates of a point after a rotation of 270° about the origin is (d)
`\(P(x,y^(\prime))\rightarrow P^(\prime)(y,-x)\)$`. So, the correct option is D.