ratio/proportion/dilation | |
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Ratio- proportional relation; rate
example: the ratio of 5 to 2, written 5:2 or 5/2
Proportion- comparative relation between things or magnitudes as to size, quantity, number, etc.
example: 2/3=6/9
Dilation- to make wider or larger; cause to expand
example:
Scale- you can find the scale by taking the coordinates of one point and finding a common relationship to the cooresponding point.
Practice Problem 1:the points of a trianlge are A(5,2), B(1,-4), and C(-1,0). they are dialated by 3.
Step 1-5(3), 2(3)= (15, 6)
Step 2-1(3), -4(3)=(3, -12)
Step 3- -1(3), 0(3)=(-3, 0)
Step 4- A' (15, 6) B' (3, -12) C' (-3, 0)
Step 2-1(3), -4(3)=(3, -12)
Step 3- -1(3), 0(3)=(-3, 0)
Step 4- A' (15, 6) B' (3, -12) C' (-3, 0)
Practice Problem 2:
21=7x/10
Step 1-Multipy both sides by 10.
210=7x
Step 2-Divide each side by 7.
x=30
Step 1-Multipy both sides by 10.
210=7x
Step 2-Divide each side by 7.
x=30
Practice Problem 3; Real World Problem: The perimeter of a pool is 408, and the ratio of its length to width is 10:7. Find the area of the pool.
Step 1-Write expressions for the length and width. The ratio 10:7 can be written as 10x and 7x.
Step 2-Write an equation to solve for x.
2l+2w=p
2(10x)+2(7x)=408
20x+14x=408
34x=408
x=12
Step 3-Length= 10x =10 (12) =120
Width=7x = 7 (12) = 84
Area= 10,080 ft.
Step 2-Write an equation to solve for x.
2l+2w=p
2(10x)+2(7x)=408
20x+14x=408
34x=408
x=12
Step 3-Length= 10x =10 (12) =120
Width=7x = 7 (12) = 84
Area= 10,080 ft.
Practice Problem 4:
2/3=x/21
Step 1- Cross multiply 3x=2(21)
3x=42
Step 2- Divide by 3
x=14