how can you model the effect of a dilation by a scale of 3 on the area of a two-dimension shape
the area will be 1 1/2 times a great
the area will be 3 times a great
the area will be 6 times as great
the area will be 9 times as great
To model the effect of a dilation by a scale of 3 on the area of a two-dimensional shape, you can use the formula:
New Area = Scale Factor^2 * Original Area
Where the scale factor is 3 in this case.
1) If the original area is A, then the new area will be:
New Area = 3^2 * A
= 9A
So, the new area will be 9 times as great as the original area.
2) If the original area is A, then the new area will be:
New Area = (3/2)^2 * A
= 9/4A
So, the new area will be 9/4 times as great as the original area, which is equal to 2.25 times.
3) If the original area is A, then the new area will be:
New Area = 3^2 * A
= 9A
So, the new area will be 9 times as great as the original area.
4) If the original area is A, then the new area will be:
New Area = (3^2) * A
= 9A
So, the new area will be 9 times as great as the original area.
In conclusion:
- The correct statement is that the area will be 9 times as great.
- The other given statements are not accurate.