If rectangle abcd, defined by the coordinates a(0, 0), b(0, -4), c(-2, -4), d(-2, 0), is dilated by a scale factor of 2, with resulting vertex a' at (2, 4), what is the center of the dilation? a) (0, 0) eliminate b) (2, 4) c) (0, -4) d) (-2, -4)

D) (-2, -4).

Step-by-step explanation:

Let be the center of dilation. Imagine that is the center of origin of a new Cartesian Plane. What would the coordinates of point A and A' on the new plane?

Dilating about the "origin" of the new plane by a factor of two will give the point , also on the new plane.

For coordinates of A' on the original plane,

.

As a result,

.

.

.

In other words, is the center of dilation.

for b its (t) and c its (d)

step-by-step explanation:

an

y = 6x -3y -12

y +3y +12 = 6x

=> . x = { 2y / 3 +2 } this is equation of line in terms of x

=> . if line meets the x-axis the co-ordinates of meeting point would be ( x , 0 )

=> . x = 2 ( 0 ) / 3 + 2

=> . x = 2

so, the point is ( 2 , 0 )