Question

Line g is dilated by a scale factor of 2 from the origin to create line g'. Where are points E' and F' located after dilation, and how are lines g and g' related?
The locations of E' and F' are E' (−8, 0) and F' (0, 4), and lines g and g' are parallel.


The locations of E' and F' are E' (−4, 0) and F' (0, 2), and lines g and g' are the same line.


The locations of E' and F' are E' (−2, 0) and F' (0, 1), and lines g and g' intersect at point F.


The locations of E' and F' are E' (−1, 0) and F' (0, 0), and lines g and g' are not related

Answer 1

Answer:

(A)The locations of E' and F' are E' (−8, 0) and F' (0, 4), and lines g and g' are parallel.

Step-by-step explanation:

Line g has the following points:

• Point E is at (-4,0)
• Point F is at (0,2)

When we dilate a line from the origin by a given factor, we multiplicate the function by that factor, so our new graph is:

y' = a*f(x)  where a is the scale factor

In this case, a=2

Therefore line g' has the following points:

$E'=2(-4,0)=(-8,0)\\F'=2(0,2)=(0,4)$

We conclude that the locations of E' and F' are E' (−8, 0) and F' (0, 4), and lines g and g' are parallel.

The correct option is A.