Find the image vertices for a dilation with center (0,0) and a scale factor of 4. (Show all Steps!!!!!)
To find the image vertices for a dilation with center (0,0) and a scale factor of 4, we first need to identify the coordinates of the original vertices. Let's say we have a shape with vertices A(1,1), B(2,3), and C(4,2).
To find the image vertices after the dilation, we need to multiply the coordinates of each vertex by the scale factor.
The formula for dilation in the coordinate plane is:
(x', y') = (kx, ky)
where (x', y') are the coordinates of the image point, (x, y) are the coordinates of the original point, and k is the scale factor.
For vertex A(1,1):
x' = 4(1) = 4
y' = 4(1) = 4
So the image vertex for A is A'(4,4).
For vertex B(2,3):
x' = 4(2) = 8
y' = 4(3) = 12
So the image vertex for B is B'(8,12).
For vertex C(4,2):
x' = 4(4) = 16
y' = 4(2) = 8
So the image vertex for C is C'(16,8).
Therefore, the image vertices for the dilation with center (0,0) and scale factor of 4 are A'(4,4), B'(8,12), and C'(16,8).