What is the percent reduction or enlargement that will result if the rule is applied to a figure on a coordinate grid? (1.5x, 1.5y)
the linear enlargement is 1.5 - 1, or 50%
The area enlargement is 1.5^2 - 1 = 125%
To calculate the percent reduction or enlargement, we need to compare the original size of the figure with the new size after applying the rule.
Let's assume the original size of the figure is A units in the x-direction and B units in the y-direction.
According to the given rule, the figure is enlarged by a factor of 1.5 in both the x-direction and the y-direction.
Therefore, the new size of the figure is 1.5 * A units in the x-direction and 1.5 * B units in the y-direction.
To calculate the percent reduction or enlargement, we can use the following formula:
Percent reduction or enlargement = ((new size - original size) / original size) * 100%
In this case, the original size is A units in the x-direction and B units in the y-direction, and the new size is 1.5 * A units in the x-direction and 1.5 * B units in the y-direction.
So, the percent reduction or enlargement in the x-direction is:
((1.5 * A - A) / A) * 100%
Simplifying this expression, we have:
(0.5A / A) * 100%
= 0.5 * 100%
= 50%
Therefore, the figure is enlarged by 50% in the x-direction.
Similarly, the percent reduction or enlargement in the y-direction can be calculated as:
((1.5 * B - B) / B) * 100%
Simplifying this expression, we have:
(0.5B / B) * 100%
= 0.5 * 100%
= 50%
Therefore, the figure is enlarged by 50% in the y-direction.
In summary, the figure is enlarged by 50% in both the x-direction and the y-direction when the rule (1.5x, 1.5y) is applied.
To determine the percent reduction or enlargement resulting from a rule applied to a figure on a coordinate grid, we need to compare the original figure to the transformed figure. In this case, the rule is given as (1.5x, 1.5y), which means that both the x and y coordinates of each point are multiplied by the factor of 1.5.
To calculate the percent reduction or enlargement, we can follow these steps:
1. Calculate the difference between the original and transformed values in both the x and y coordinates. In this case, the difference would be (1.5x - x) and (1.5y - y).
2. Calculate the ratio between the differences and the original values. The ratio would be [(1.5x - x) / x] and [(1.5y - y) / y].
3. Calculate the average of the two ratios found in the previous step by adding them together and dividing by 2. The average would be [((1.5x - x) / x) + ((1.5y - y) / y)] / 2.
4. Convert the average ratio to a percentage by multiplying it by 100. This will give us the percent reduction or enlargement resulting from the given rule.
Applying these steps to the given rule (1.5x, 1.5y):
1. The difference in the x coordinate would be (1.5x - x) = 0.5x.
2. The difference in the y coordinate would be (1.5y - y) = 0.5y.
3. The average ratio would be [((0.5x) / x) + ((0.5y) / y)] / 2 = (0.5 + 0.5) / 2 = 1.
4. The percent reduction or enlargement would be 1 * 100 = 100%.
Therefore, applying the rule (1.5x, 1.5y) would result in a 100% enlargement of the figure on the coordinate grid.