The point (-4,1) is rotated 180 degrees counterclockwise using center (-3,0). What are the coordinates of the image? (my teacher didn't include an image so im sorry if you were wanting one)

A. (-4, -1)

B. (-5, -2)

C. (-2, -1)

D. (4, -1)

  C.  (-2, -1)

Step-by-step explanation:

It can help to plot the points.

For rotation 180 degrees, the center of rotation is the midpoint of the segment joining the given point and its image. That means you want to find the other end of a segment with one end (-4, 1) and midpoint (-3, 0).

For center of rotation O, this means ...

  O = (A +A')/2

  2O -A = A'

  A' = 2(-3, 0) -(-4, 1) = (-6+4, 0 -1) = (-2, -1)

The coordinates of the image are (-2, -1).

hello,

b) 62.47% of the students are between 14 and 18 years old.

step-by-step explanation:

mean = 15 and standard deviation = 2

student between 14 to 18

formula used z-score

for age 14 , z score

using z-table , p(z> -0.5)=0.3085

for age 18 , z score

using z-table , p(z< 1.5)=0.9332

p(-0.5< z< 1.5)=0.9332-0.3085 = 0.6247

thus, 62.47% of the students are between 14 and 18 years old.

click to let others know, how is it

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