Line g is dilated by a scale factor of one half from the origin to create line g'. Where are points E' and F' located after dilation, and how are lines g and g' related?

A. The locations of E' and F' are E' (−8, 0) and F' (0, 4), and lines g and g' intersect at point F.
B. The locations of E' and F' are E' (−4, 0) and F' (0, 2), and lines g and g' are the same line.
C. The locations of E' and F' are E' (−2, 0) and F' (0, 1), and lines g and g' are parallel.
D. The locations of E' and F' are E' (−1, 0) and F' (0, 0), and lines g and g' are not related.

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

Step-by-step explanation:

If we have the graph of the equation y = f(x)

A dilation from the origin by a given factor, means that we multilpicate the function by that factor, so our new graph is:

y' = a*f(x)

where a is the scale factor, here a = 1/2.

so g' = (1/2)*g

then if E = (-4, 0)

          E' = (1/2)*E = (-2, 0)

          F = (0, 2)

          F' = (1/2)*F = (1, 0)

Then the correct option is C The locations of E' and F' are E' (−2, 0) and F' (0, 1), and lines g and g' are parallel.

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