Use the graph at the right. Find the vertices of the image of QRTW for a dilation with center (0,0) and a scale factor of
(1/5).
Q: (-3,4)
R: (-2,-2)
T: (3,1,)
W: (3,5)
just multiply all coordinates by 1/5
To find the vertices of the image of QRTW after a dilation with a center at (0,0) and a scale factor of 1/5, we will need to multiply the coordinates of each vertex by the scale factor.
The scale factor indicates how much the coordinates should be multiplied. In this case, the scale factor is 1/5.
Let's calculate the image of each vertex:
For Q(-3,4):
- Multiply the x-coordinate (-3) by the scale factor (1/5): -3 * 1/5 = -3/5
- Multiply the y-coordinate (4) by the scale factor (1/5): 4 * 1/5 = 4/5
The image of Q is (-3/5, 4/5).
For R(-2,-2):
- Multiply the x-coordinate (-2) by the scale factor (1/5): -2 * 1/5 = -2/5
- Multiply the y-coordinate (-2) by the scale factor (1/5): -2 * 1/5 = -2/5
The image of R is (-2/5, -2/5).
For T(3,1):
- Multiply the x-coordinate (3) by the scale factor (1/5): 3 * 1/5 = 3/5
- Multiply the y-coordinate (1) by the scale factor (1/5): 1 * 1/5 = 1/5
The image of T is (3/5, 1/5).
For W(3,5):
- Multiply the x-coordinate (3) by the scale factor (1/5): 3 * 1/5 = 3/5
- Multiply the y-coordinate (5) by the scale factor (1/5): 5 * 1/5 = 5/5 = 1
The image of W is (3/5, 1).
Therefore, the vertices of the image of QRTW after the dilation with a center at (0,0) and a scale factor of 1/5 are:
Q'(-3/5, 4/5)
R'(-2/5, -2/5)
T'(3/5, 1/5)
W'(3/5, 1)