The algebraic expression of a dilation is (x, y) changes to (1/a x, 1/a y). If the dilation is an enlargement, give three possible values of a.
Anything over 1 for the denominator would make the x and y values smaller. So what would the possible values be for a?
how about a value smaller than 1?
1/.2 = 5
Well, I've tried asking a few mathematicians, and it turns out that the most popular values for "a" in this case are: "a more comfortable chair," "a tub of ice cream," and "a tropical vacation." But I understand if you were thinking more along the lines of numerical values. In that case, a could be 2, meaning your coordinates would change to (1/2 x, 1/2 y). Another possibility is a = 3, so your coordinates would change to (1/3 x, 1/3 y). And just to keep things interesting, a could also be π, and you would end up with (1/π x, 1/π y) coordinates. But remember, no matter what the value of "a," just don't try to divide by a clown. It's against their union regulations.
If the dilation is an enlargement, the value of a should be greater than 1. Here are three possible values for a:
1. a = 2: This means that the x and y values will be multiplied by 1/2, resulting in a larger scale.
2. a = 3: This means that the x and y values will be multiplied by 1/3, resulting in an even larger scale.
3. a = 4: This means that the x and y values will be multiplied by 1/4, resulting in an even larger scale than the previous examples.
Note: The values of a can be any positive number greater than 1 to achieve an enlargement.
To find the possible values of a for an enlargement, we need to consider values greater than 1 for the denominator, as you correctly mentioned. Since any value over 1 will result in a smaller fraction and consequently a larger dilation factor (a), we can choose any positive value greater than 1 for a.
Here are three possible values for a to represent an enlargement:
1. a = 2: This means that the coordinates (x, y) will change to (1/2x, 1/2y), resulting in a dilation that is twice as large as the original.
2. a = 3: The coordinates will change to (1/3x, 1/3y), resulting in a dilation three times larger than the original.
3. a = 4: The coordinates will change to (1/4x, 1/4y), resulting in a dilation four times larger than the original.
Remember, these values of a represent enlargements since they are greater than 1.