Suppose you are given a bottle of water and three beakers. One of the beakers holds 30mL, one holds 40mL, and the largest of three beakers holds 200mL when full. There aren't any markings on any of the beakers. Describe how you could put exactly 20 mL of water in the large beaker without using any other equipment.

Answer:

The image of point (x , y) by dilation with center origin and scale factor k is (kx , ky)

Step-by-step explanation:

* Lets talk about dilation

- A dilation is a transformation that changes the size of a figure.  

- It can become larger or smaller, but the shape of the

 figure does not change.  

- The scale factor, measures how much larger or smaller  

  the image will be

- If the scale factor greater than 1, then the image will be larger

- If the scale factor between 0 and 1, then the image will be smaller

* In a problem  of dilation

∵ The center of dilation is the origin

∵ The scale factor of dilation is k

∵ The point is (x , y)

- In dilation with center origin and scale factor k to find the image

 of the point multiply each coordinates of the point by the scale

 factor k because the distance d between the point and the

 origin will be equal kd which is the distance between the origin

 and the image of the point d is depending on the coordinates

 of the point

∴ The image of point (x , y) by dilation with center origin and

   scale factor k is (kx , ky)

* Ex: If point A is (3 , 4)

∵ The distance from the origin to point A =

∵ The scale factor of dilation is 2 and the center is the origin

∴ The image of A is A' = (3 × 2 , 4 × 2) = (6 , 8)

∵ The distance from the origin to point A' =

∵ 10 ÷ 5 = 2 which is the value of the scale factor

∴ The image of point (x , y) by dilation with center origin and

   scale factor k is (kx , ky)

Answer:

It will take 13 years until Ishaan is only 5 times as old as William.