Question

enlargement
reduction
what is the scale factor? *
1 point
1/3
1/2
2
3
4
if p=(4,2) what is the coordinate of p? *
1 point
(8,4)
(8,2)
(-8,4)
(-2,-8)

Explanation:

Step1: Identify transformation type

The image of the shape is larger than the original, so it is an enlargement.

Step2: Find scale - factor

Let's take a point and its image. For example, if we consider a point on the original shape and its corresponding point on the enlarged shape. If we assume the origin as the center of dilation, and we know that if a point $(x,y)$ is dilated by a scale - factor $k$ to get $(x',y')$, then $x'=kx$ and $y' = ky$. By comparing the lengths of corresponding sides of the original and the enlarged shape, we can see that the scale - factor $k = 2$. For example, if we consider a line segment of length 1 unit in the original shape, its corresponding line segment in the enlarged shape has length 2 units.

Step3: Find coordinates of $P'$

Given $P=(4,2)$ and scale - factor $k = 2$. Using the formula for dilation $(x',y')=k(x,y)$, we substitute $x = 4$, $y = 2$ and $k = 2$. So $x'=2\times4 = 8$ and $y'=2\times2 = 4$. Thus, the coordinates of $P'$ are $(8,4)$.

Answer:

1. Enlargement
2. 2
3. (8, 4)