In geometry, dilation means to resize a shape. It means either to make a shape larger or smaller.
Dilations can be applied to parallel lines. Here is an example.
Line ℓ has the equation y = -2x + 2. Write the equation of the image of ℓ after dilation with a scale factor of 4, centered at the origin.
To answer this question, we first need to find 2 points on line ℓ. We have
(0, 2)
(1, 0)
Now, we apply the dilation (x, y) = (4x, 4y):
(0, 2)= (0, 8)
(1, 0) = (4, 0)
Since (0, 8) and (4, 0) are the 2 points on line ℓ', the slope of ℓ' is
(y2-y1) / (x2-x1) = (0-8) / (4-0) = -2.
since ℓ' has a slope of -2 and a y-intercept of 8, the equation of ℓ' is y=-2x+8