Suppose that triangle ABC is dilated to A'B'C' by a scale factor of 4 with a center of dilation at the origin. What is the distance from the center of dilation to the midpoint of B'C'?

The distance from the center of dilation to the midpoint of B'C' would be an increase in the initial distance from the origin to midpoint of BC by a scale factor of 4.

Step-by-step explanation:

Dilation is a transformation process that increases the size of a given figure by a factor. This implies that every coordinate of the initial figure would be multiplied by the factor to produce the new figure.

In the given question, dilation of the triangle at the origin by a factor of 4 implies that the coordinates of the triangle increased by a factor of 4. Thus, the distance from the center of dilation to the midpoint of B'C' would be an increase in the initial distance from the origin to midpoint of BC by a scale factor of 4.

answer: 230 miles ( vote ! )

step-by-step explanation:

180.39 minus 17.99 equals 162.4

then divide 162.4 by .80 to get 230

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1