A figure is dilated by a scale factor of 3. If the origin is the center of dilation, what is the image of a vertex located at (3
1 answer:
Answer:
(9,12).
Step-by-step explanation:
If a figure dilated by a scale factor of k and origin is the center of dilation, then the relation between point and its image is defined as
It is given that a figure is dilated by a scale factor of 3 and origin is the center of dilation. So,
We need to find the image of a vertex located at (3, 4). So, substitute x=3 and y=4 in the above rule of dilation.
Therefore, the image of a vertex located at (3, 4) is (9,12).
You might be interested in
You can find counterexamples to disprove this claim. We have positive integers that are perfect square numbers; when we take the square root of those numbers, we get an integer.
For example, the square root of 1 is 1, which is an integer. So if y = 1, then the denominator becomes an integer and thus we get a quotient of two integers (since x is also defined to be an integer), the definition of a rational number.
Example: x = 2, y = 1 ends up with which is rational. This goes against the claim that
is always irrational for positive integers x and y.
Any integer y that is a perfect square will work to disprove this claim, e.g. y = 1, y = 4, y= 9, y = 16. So it is not always irrational.