Please help, I’m stuck and need help with these!
1. The point (1, 1) is the image under the translation (x, y) --> (x + 3, y - 3). what is the preimage of this point?
2. A dilation has center (0, 0, 0). find the image point of (-1, -2, 0) for the scale factor of 3.
so x+3 = 1 and y-3 = 1
x = -2 and y = 4
the original point was (-2,4)
(x,y,z) ---> (3x,3y,3z)
so (-1, -2, 0) ----> .........
I’m kinda confused still.
(-4, -5, 3)???
Sure! I'd be happy to help you with these questions. Let's break them down one by one:
1. The point (1, 1) is the image under the translation (x, y) --> (x + 3, y - 3). What is the preimage of this point?
To find the preimage of a point under a translation, we need to apply the opposite translation. In this case, the opposite translation of (x, y) --> (x + 3, y - 3) would be (x, y) --> (x - 3, y + 3).
So, to find the preimage of the given point (1, 1), we substitute the values into the opposite translation equation:
(x, y) = (1 - 3, 1 + 3) = (-2, 4)
Therefore, the preimage of the point (1, 1) under the translation (x, y) --> (x + 3, y - 3) is (-2, 4).
2. A dilation has a center (0, 0, 0). Find the image point of (-1, -2, 0) for the scale factor of 3.
To find the image point of a given point under a dilation, we need to multiply each coordinate by the scale factor. In this case, the scale factor is 3.
The formula for a dilation with a center (0, 0, 0) is given by (x, y, z) --> (kx, ky, kz), where k is the scale factor.
Applying this to the given point (-1, -2, 0) with a scale factor of 3, we have:
(x, y, z) = (3 * -1, 3 * -2, 3 * 0) = (-3, -6, 0)
Therefore, the image point of (-1, -2, 0) under the dilation with a center (0, 0, 0) and a scale factor of 3 is (-3, -6, 0).
I hope this helps! Let me know if you have any further questions.