Question

Triangle END is translated using the rule (x,y)→(x-4, y-1) to create triangle E'N'D'. If a line segment is drawn from point E to point E' and from point N to point N', which statement would best describe the line segments drawn? . Select one:. a. They are parallel and congruent.. b. They are perpendicular to each other.. c. They share the same midpoints.. d. They create diameters of concentric circles.

Answer 1

The correct answer is:

A) They are parallel and congruent.

Explanation:

Two lines are parallel if they have the same slope. Since the lines we are drawing are from the pre-image point to the image point, the slope will be the ratio of the vertical part of the translation to the horizontal part of the translation. For each set of points, this will be -1/-4, or 1/4; this means the slopes are the same, so the lines are parallel.

To determine if the segments are congruent, we would use the distance formula:

$d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}$

Subtracting the y-coordinates tells us the vertical distance between points. However, since the same translation is applied to each point, the vertical distance will always be the same (-1).

Subtracting the x-coordinates tells us the horizontal distance between point. However, since the same translation is applied to each point, the horizontal distance will always be the same (-4).

Since the horizontal and vertical distances are the same, we will get the same value for the distance formula between any two points mapped this way. This means the segments are congruent.

Answer 2

The best statement that would describe the line segments is Letter A. The triangle END is translated using the rule (x,y) > (x-4,y-1) to create triangle E'N'D. if a line segment is drawn from point E to point E' and from point N to point N' are "parallel and congruent".