On a number line, the coordinates of D,E,F,G, and H are -9, -2, 3, 0, 3, and 5, respectively. Find the lengths of the two segments. Then tell whether they are congruent.

Hi there! Thank you for the opportunity to help you with your question!

(Quick comment first: You say there are five coordinates, DEFGH, but you give six locations (-9,-2,3,0,3,5). I'm assuming there is a typo somewhere...)

The length of a line segment is given by the distance between two points. The distance between two points on a number line is given by the absolute value of their difference.

For the segment DG

The length of the segment DG is given by the absolute value of the difference between the two points. Since G is located at 0, and D is located at -9, the difference is equal to 3 - (-9) = 3 + 9 = 12.

For the segment DH

The length of the segment DH is again given by the difference between the two points. Now, H is located at 5, and D is located at -9, so the difference is equal to 5 - (-9) = 14.

Are the two segments congruent? The two segments are not congruent, because they have different lenghts.

Please let me know if you need any clarification. Always glad to help!