30 POINTS

Charles plots the point with the polar coordinates (−5,−3π/4). How does he plot this point?

Charles first determines which line the angle of rotation places the point on. This line tells Charles that the point must lie in _ a if r is positive or _ if r is negative.

The radius of 5 tells Charles that the point lies on the fifth circle of the polar plane. The value of r is negative. Therefore, the point will lie _ the angle of rotation.

This line tells Charles that the point must lie in Quadrant 3 if r is positive or Quadrant 1 if r is negative.

The value of r is negative. Therefore, the point will lie in the opposite quadrant as the angle of rotation.

Step-by-step explanation:

With polar coordinates the first value represents the distance from the origin and the second value represents the rotation from 0. In this case the distance from the origin value is negative, which means it will be in the opposite quadrant to the angle of rotation.

(-5, −3π/4) results in the same point as (5, π/4)

A rotation of −3π/4 results in the same rotation as 5π/4

The rotation results in Quadrant 3 but because the distance value is negative the final resulting point is in Quadrant 1.

the range is 19

step-by-step explanation:

the range is biggest number minus the smallest, so in this case it would be

41 - 22 = 19

"image"

step-by-step explanation:

in most of these problems, the notation is that the point with a "prime" is the image of the point without. that is, b' is the image of b.

here, there is no dilation or reflection. there is simply translation (with no direction shown). which figure you call the "preimage" and which one you call the "image" is up to you. as a matter of convention, the naming is as described above.