triangle J'K'L' shown on the grid below a dilation of triangle JKL using the origin as the center of dilation:

The scale factor used to create triangle ΔJ'K'L', is 3

The reason for arriving at the above scale factor is as follows;

The known parameters:

The vertices of the triangle ΔJKL are:

J(2, 4), K(3, 2), and L(4, 3)

The vertices of the triangle ΔJ'K'L' are:

J'(6, 12), K'(9, 6), and L'(12, 9)

The required parameter:

The scale factor used to create ΔJ'K'L'

The strategy:

Find and divide the lengths of the sides of ΔJ'K'L', by the calculated lengths of the sides of the triangle ΔJKL as follows;

The lengths of the segments in ΔJKL are;

JK = √((3 - 2)² + (2 - 4)²) = √5

KL = √((4 - 3)² + (3 - 2)²) = √2

JL = √((4 - 2)² + (3 - 4)²) = √5

The lengths of the segments in ΔJ'K'L' are;

J'K' = √((9 - 6)² + (6 - 12)²) = √(45) = 3·√5

K'L' = √((12 - 9)² + (9 - 6)²) = √(18) = 3·√2

J'L' = √((12 - 6)² + (9 - 12)²) = √(45) = 3·√5

Therefore, we get;

The scale factor used to create triangle triangle ΔJKL from triangle ΔJ'K'L' , S.F. = 3

Learn more about scale factors here:

link

 b) 3

Step-by-step explanation:

From K to L the y-length is 2 and the x-length is 1

From K' to L' the y-length is 6 and the x-length is 3

Therefore, J'K'L' is 3 times as large as JKL so the dilation is 3.

a. the residual plot for model 1 has a random pattern and is a good fit for the data.

g = (2, 2)

step-by-step explanation:

given the ratio is 1 : 1 then f is the midpoint of eg

let the coordinates of g = (x, y)

using the midpoint formula

(0 + x) = 1 ( multiply both sides by 2 )

0 + x = 2 ⇒ x = 2

similarly

(4 + y) = 3 ( multiply both sides by 2 )

4 + y = 6 ( subtract 4 from both sides )

y = 2

coordinates of g = (2, 2)