Arectangle on the coordinate plane has vertices at (0,0), (3,0), (3,2), and (0,2). a dialation of the rectangle has vertices at (0,0), (9,0), (9,6), and (0,1). find the scale factor

The scale factor is 3.

Step-by-step explanation:

1. You kwnow that original rectangle has the following coordinates in its vertices:

 (0,0), (3,0), (3,2), and (0,2)

2. After dilation, the rectangle has vertices at (0,0), (9,0), (9,6), and (0,1). Therefore, you can calculate the scale factor as following:

Let's call the scale factor and let's choose one the coordinates of the original rectangle and the same coordinate after dilation:

Original vertex: (3,2) ; Vertex after dilation: (9,6)

Then:

The scale factor is 3.

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!

is this part of a question or something