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? F g E -5 -2 -1 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 Flare E' (-4, 0) and F'(0, 2), and lines g and g are the same line. O The locations of E' and Fare E' (-2, 0) and F'(0, 1), and lines g and g intersect at point F. The locations of E' and Fare E' (-1, 0) and F'(0, 0), and lines g and g' are not related.​

Answer 1

After a dilation from the origin by a scale factor of 2, the coordinates of points E and F on line g would become E'(-4, 0) and F'(0, 4), making lines g and g' parallel to each other.

Step-by-step explanation:

To determine where points E and F are located after dilation with a scale factor of 2 from the origin, we need to apply the scale factor to their original coordinates. If E and F are points on line g with coordinates E(-2, 0) and F(0, 2) respectively, then after dilation, their coordinates would become E'(-4, 0) and F'(0, 4).

Furthermore, since the dilation is performed from the origin, line g' would be parallel to line g. This is due to the fact that dilation from the origin preserves the angles between lines. Therefore, the correct answer would be that the locations of E' and F' are E' (-4, 0) and F'(0, 4), and lines g and g' are parallel.

Answer 2

After a dilation of line g by a scale factor of 2 from the origin, point E moves to E' (-4, 0) and F moves to F' (0, 2), with line g' remaining parallel to line g.

Step-by-step explanation:

When a line is dilated by a scale factor from the origin, each point on the line is moved away from the origin by that scale factor. If the original points are E(-2, 0) and F(0, 1), after a dilation by a scale factor of 2, the new locations for E' and F' would be twice the distance from the origin. Therefore, E' would be at (-4, 0) and F' at (0, 2), given that we double both the x and y coordinates for each point respectively.

As for how lines g and g' are related, it's important to note that when a line is dilated from the origin, the new line g' remains parallel to the original line g. This is because all points are consistently scaled from the origin, preserving the slope and therefore the parallel relationship.