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?
coordinate plane with point E at negative 4 comma 0 and point F at 0 comma 2, line g intersects points E and F


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:

The points where E' and F' are located after dilation and how the lines g and g' are related are;

The locations E' and F' are E'(-8, 0) and F'(0, 4), and lines g and g' are parallel

Please see attached plot of lines g and g' created with MS Excel

Step-by-step explanation:

When an object is dilated by a scale factor, the length of the sides of the image formed is given as follows;

The length of the image = The length of the figure × The scale factor

The given parameters are;

The center of dilation = (0, 0) Dilated from the origin

The coordinates of the endpoint of the line 'g' = E(-4, 0), F(0, 2)

Therefore, we have;

The 'x', and 'y' coordinates of the point E' on the image from the center of dilation  (0, 0) = (-4 × 2, 0 × 2) = (-8, 0)

The 'x', and 'y' coordinates of the point F' on the image from the center of dilation  (0, 0) = (0 × 2, 2 × 2) = (0, 4)

Therefore, the coordinates of the point E' and F' on line g' = E'(-8, 0) and F'(0, 4)

Given that the proportion of the distances of E and E' to center of dilation (to the origin) and F and F' center of dilation are equal by the triangle proportionality theorem, EF is parallel to E'F' and the lines g and g' are said to be parallel

Therefore;

The coordinate of point E' = (-8, 0) and The coordinate of point F' = (0, 4)

Ling g is parallel to line g'