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' =

Question

asked Jan 19, 2022 90.0k views

1 Answer

OttherCreek · Answer 1 · 2022-01-25T10:55:35+0000

Answer:

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.

- 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) .