Given a dilation with the origin O (0, 0), by observation determine the scale factor "K."
DO, K = (5, 0) (10, 0)
The dilation an expansion.
true or false
Idk
To determine the scale factor "K" for a dilation, we can observe the change in distance between the origin O (0, 0) and the given points after the dilation.
In this case, the points are (5, 0) and (10, 0).
The distance between the origin O (0, 0) and the point (5, 0) is 5 units.
The distance between the origin O (0, 0) and the point (10, 0) is 10 units.
Since the distance has doubled after the dilation, we can conclude that the scale factor "K" is 2.
Therefore, the statement that the dilation is an expansion is true.
To determine the scale factor, we can observe the change in coordinates after the dilation.
In this case, we are given the original point O(0,0) and two points after dilation: D(5,0) and K(10,0).
To find the scale factor, we can observe the change in x-coordinate from the origin to D and K.
For the x-coordinate, the change from O to D is 5-0 = 5 and the change from O to K is 10-0 = 10.
We can see that the change in x-coordinate for D and K is equal, which indicates that the scale factor is the same for both points.
Thus, the scale factor "K" for this dilation is 5.
Now, let's answer the second part of your question. You mentioned that the dilation is an expansion.
To determine whether the dilation is an expansion or a contraction, we can check if the scale factor is greater than 1 (expansion) or less than 1 (contraction).
In this case, the scale factor is 5, which is greater than 1. Therefore, the dilation is an expansion.
So, the correct answer is true, the dilation is an expansion.
The dilation constant K with origin (0,0) can be determined by
x'/x or y'/y
where (x,y) is the original position, and (x',y') is the image (dilated position).
In this case, since both y' and y are zero, only k=x'/x applies.