Question

Find the new set of coordinates given the scale factor for k > 1. E = (-1, -2), F = (2, -5), G = (5, -1), H = (1, 1) Scale factor = 6 E'= F' = G' = H' =

Answer 1

The new set of coordinates are
`E'(x,y) = (-6,-12)`,
`F'(x,y) = (12,-30)`,
`G'(x,y) = (30,-6)` and
`H'(x,y) = (6,6)`.

Explanation:

Vectorially speaking, dilation can be defined by this equation:

`D'(x,y) = O(x,y) +k\cdot (D(x,y)-O(x,y))` (1)

Where:

`O(x,y)` - Center of dilation.

`D(x,y)` - Original point.

`k` - Scale factor.

`D'(x,y)` - Dilated point.

Let suppose that center of dilation is located at origin, we determine the new set of coordinates below:

`E'(x,y) = O(x,y) +k\cdot (E(x,y)-O(x,y))`

`E'(x,y) = (0,0) +6\cdot (-1,-2)`

`E'(x,y) = (-6,-12)`

`F'(x,y) = O(x,y) + k\cdot (F(x,y)-O(x,y))`

`F'(x,y) = (0,0) +6\cdot (2,-5)`

`F'(x,y) = (12,-30)`

`G'(x,y) = O(x,y) + k\cdot (G(x,y)-O(x,y))`

`G'(x,y) = (0,0) + 6\cdot (5,-1)`

`G'(x,y) = (30,-6)`

`H'(x,y) = O(x,y) +k\cdot (H(x,y)-O(x,y))`

`H'(x,y) = (0,0) + 6\cdot (1,1)`

`H'(x,y) = (6,6)`

The new set of coordinates are
`E'(x,y) = (-6,-12)`,
`F'(x,y) = (12,-30)`,
`G'(x,y) = (30,-6)` and
`H'(x,y) = (6,6)`.