Arectangle is dilated by a factor of 4. each point in the image is from the origin as its corresponding pre-image point. from the following, which is the corrent a. eight times further b. four times further c. four times closer d. eight times closer

Option: B is the correct answer.

B.    four times further

It is given that:

A rectangle is dilated by a factor of 4.

This means that each of the side of the rectangle is increased by a multiple of 4 i.e. the image of the figure enlarges.

This means that the distance of any point in the image from the origin will be four times the distance of it's corresponding point in the original figure from the origin.

              Hence the answer is: Option: B

i believe the answer is the polygon, heptagon.

the largest number of the four options is 1.8 x 10-2

you have it in scientific notation.

1.80 x 10-6   = 0.00000180

1.80 x 10-4   = 0.000180 (bigger, or "less small", than the former one)

so

1.8 x 10-2       = 0.0180. as you see. the "less small", or the biggest one of them all.

as you have negative exponent, it means you are dividing 1.8 by 100 (i.e. moving the dot towards left, two times).

if you had positive exponent for the scientific notation, power of tenths, you would be multiplying times 100 (moving the dot towards right) as below:

1.8 x (10)2 = 180

so. if you have negative exponent in scientific notation, move the dot toward left. if it is positive, toward right as many times the exponent tells you.