Question

G, H, and K are three points on a number line. The coordinates of G and H are 4 and -3 respectively. If H is between G and K and GK = 13, what is the coordinate of K?

Answer 1

To find the coordinate of point K on the number line, calculate the distance from G to H (GH), then subtract this from the total distance from G to K (GK) to get the distance from H to K (HK), and finally add this distance to H's coordinate.

Step-by-step explanation:

The student is trying to find the coordinate of point K on a number line, given that G has a coordinate of 4, H is between G and K at the coordinate -3, and the distance from G to K (GK) is 13.

Step-by-step Solution

1. First, find the distance GH, which is the distance between G and H on the number line. GH = |4 - (-3)| = |4+3| = 7.
2. Since GK = 13 and GH is part of this distance, we must subtract GH from GK to find HK (the distance from H to K). So, HK = GK - GH = 13 - 7 = 6.
3. As H is at -3 and K is to the right of H, the coordinate of K will be 6 units to the right of -3, thus K = -3 + 6 = 3.

The coordinate of point K is 3.