Square rstu is shown below with a line ab drawn through it's center. if the square is dilated using the scale factor of 1/4 and a line is drawn through the center of the new dilated figure, what relationship will that line have with line ab in the drawing below

The new line segment CD is 1/4 th of AB

CD = × AB

Step-by-step explanation:

Given that, RSTU is a square and AB a line drawn through it's center.

let the length of side of square be a.

⇒ Length of line segment AB = a. (as it is same as length of side of square)

Now, given the square is dilated using the scale factor of 1/4 and a line is drawn through the center of the new dilated figure.

let this line be CD with points C and D on sides of dilated square.

Now, as the square is dilated by a factor of 1/4, length of side of dilated square is a× =

⇒ the length of CD =

⇒ The new line segment CD is 1/4 th of AB

CD = × AB

18

step-by-step explanation:

draw the shape and you will see that f and k are actually at adjacent vertices (points of the hexagon that are neighboring).   so find the distance between (1,2) and (4,2).   that is easy since (1,2) and (4,2) is just a vertical distance to count, which is 3.   it is a regular polygon which means all sides are congruent.   you have 6 sides (hexa) so multiply 6 by 3 to receive 18.