What time is it when the small hand is in between the 8 and 9 and when the big hand is at the 6?
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Answer:
The dilation on any point of the rectangle is .
Step-by-step explanation:
From Linear Algebra, we define the dilation of a point by means of the following definition:
(1)
Where:
- Coordinates of the point G, dimensionless.
- Center of dilation, dimensionless.
- Scale factor, dimensionless.
- Coordinates of the point G', dimensionless.
If we know that ,
and
, then scale factor is:
The dilation on any point of the rectangle is:
(2)
The dilation on any point of the rectangle is .
3:5 ratio mean there are 8 "parts" (3 + 5 = 8)
The distance between the x-coordinates is |-3 - 5| = 8.
So each "part" is 8/8 = 1 unit long in the x-direction.
You want I to be 3(1) = 3 units from D, so the x-coordinate of I is -3 + 3 = 0.
Same deal for y.
|2 - 5| = 3 is the distance between D and E
Each part is 3/8.
3(3/8) = 9/8
2 + 9/8 = 25/8
So the point I is (0, 25/8)
The distance between the x-coordinates is |-3 - 5| = 8.
So each "part" is 8/8 = 1 unit long in the x-direction.
You want I to be 3(1) = 3 units from D, so the x-coordinate of I is -3 + 3 = 0.
Same deal for y.
|2 - 5| = 3 is the distance between D and E
Each part is 3/8.
3(3/8) = 9/8
2 + 9/8 = 25/8
So the point I is (0, 25/8)