Question

The diameter of a circle was 12 cm and the diameter of the final circle was 84 cm. What is the scale factor?

Answer 1

What are the coordinate points of (4, 7) if A undergoes a rotation of:


90° clockwise
180° clockwise
270° clockwise

Answer 2

Find the dilation of 4 with center (0, 0) for the following points if A(−1, 2) B(−4, −3)

Answer 3

What are the coordinates of point C' if C (−1, 6) is rotated 270° clockwise around the origin?
Your answer must be listed as a coordinate so use parenthesis.
C'=

Answer 4

The scale factor can be found by dividing the final diameter by the initial diameter.

Final diameter = 84 cm
Initial diameter = 12 cm

Scale factor = Final diameter / Initial diameter = 84 cm / 12 cm = 7

Therefore, the scale factor is 7.

Answer 5

To find the new coordinates after a rotation, we can use the rotation formulas.

90° clockwise rotation:
The new x-coordinate is given by: x' = y
The new y-coordinate is given by: y' = -x

For the point (4, 7):
x' = 7
y' = -4

Therefore, after a 90° clockwise rotation, the new coordinates are (7, -4).

180° clockwise rotation:
The new x-coordinate is given by: x' = -x
The new y-coordinate is given by: y' = -y

For the point (4, 7):
x' = -4
y' = -7

Therefore, after a 180° clockwise rotation, the new coordinates are (-4, -7).

270° clockwise rotation:
The new x-coordinate is given by: x' = -y
The new y-coordinate is given by: y' = x

For the point (4, 7):
x' = -7
y' = 4

Therefore, after a 270° clockwise rotation, the new coordinates are (-7, 4).

Answer 6

To find the dilation of a point, multiply the coordinates of the point by the scale factor.

For a dilation of 4 with center (0, 0):

For point A(-1, 2):
New x-coordinate: -1 * 4 = -4
New y-coordinate: 2 * 4 = 8

Therefore, the new coordinates of point A after the dilation are (-4, 8).

For point B(-4, -3):
New x-coordinate: -4 * 4 = -16
New y-coordinate: -3 * 4 = -12

Therefore, the new coordinates of point B after the dilation are (-16, -12).

Answer 7

To rotate a point (x, y) 270° clockwise around the origin, we can apply the rotation formulas:

For a 270° clockwise rotation:
The new x-coordinate is given by: x' = -y
The new y-coordinate is given by: y' = x

For point C (-1, 6):
New x-coordinate: x' = -6
New y-coordinate: y' = -1

Therefore, after rotating C (-1, 6) 270° clockwise around the origin, the new coordinates are C'(-6, -1).