Question

geometry
a) in mathematics, the word “dilate” means to enlarge or reduce.
b) the word “translate” means to slide a figure.
c) the word “reflect” means to flip a figure.
d) the word “rotate” means to turn a figure around a point.

1. dilate the figure by a scale factor of 2 with the center of dilation at the origin. record the coordinates of the original figure and the new image, and then graph the new image.

j ( , ) k( , ) l( , )
j( , ) k( , ) l( , )

1. reflect the figure across x
2. translate the figures following the rules given:

a. (x, y) -> (x - 2, y + 6)
b. (x, y) -> (x + 3, y - 3)

Explanation:

Step1: Identify original coordinates

Assume from the graph, \(J(1,4)\), \(K(1,1)\), \(L(3,1)\)

Step2: Apply dilation formula

For a dilation with scale - factor \(k = 2\) and center of dilation at the origin \((x,y)\to(kx,ky)\).
For point \(J(1,4)\), \(J'(2\times1,2\times4)=(2,8)\)
For point \(K(1,1)\), \(K'(2\times1,2\times1)=(2,2)\)
For point \(L(3,1)\), \(L'(2\times3,2\times1)=(6,2)\)

Answer:

\(J(1,4)\), \(K(1,1)\), \(L(3,1)\)
\(J'(2,8)\), \(K'(2,2)\), \(L'(6,2)\)