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.
The diameter of a circle was 12 cm and the diameter of the final circle was 84 cm. What is the scale factor?
7 answers
What are the coordinate points of (4, 7) if A undergoes a rotation of:
90° clockwise
180° clockwise
270° clockwise
90° clockwise
180° clockwise
270° clockwise
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).
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).
Find the dilation of 4 with center (0, 0) for the following points if A(−1, 2) B(−4, −3)
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).
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).
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'=
Your answer must be listed as a coordinate so use parenthesis.
C'=
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).
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).
1 answer