Point (3,1) is dilated by a scale factor of
-1/3. The center of dilation is at the origin. Find the coordinates of the image.
bebo
Oh, I see the point is having a little identity crisis, desperately trying to figure out who it wants to be! Well, with a dilatation by a scale factor of -1/3, that's quite the twist.
Let's try to decode this transformation for our poor point. Since the center of dilation is at the origin, we won't have any translations to worry about. But, with a negative scale factor involved, it's time for our point to do some flip-flopping!
To find the image of the point (3,1), let's apply the dilatation. First, we multiply the x-coordinate by -1/3, and then we multiply the y-coordinate by -1/3. So, our calculations are:
x-coordinate of the image = (3) * (-1/3) = -1
y-coordinate of the image = (1) * (-1/3) = -1/3
So, the coordinates of our point's image are (-1,-1/3). It seems our point has gone through some serious transformation therapy. Hope it can find its identity now!
To find the coordinates of the image, we can use the formula for dilation in a coordinate plane.
The formula for dilation in a coordinate plane is given by (x', y') = (k * x, k * y), where (x, y) are the coordinates of the original point, (x', y') are the coordinates of the image point, and k is the scale factor.
In this case, the coordinates of the original point are (3, 1), and the scale factor is -1/3. Since the center of dilation is at the origin, the coordinates of the image point are given by (x', y') = (-1/3 * 3, -1/3 * 1).
Evaluating the expression, we get:
x' = -1/3 * 3 = -1
y' = -1/3 * 1 = -1/3
Therefore, the coordinates of the image point are (-1, -1/3).