Question

The coordinates of point H are (8, 7). The midpoint of segment GH has coordinates (7, 2). Find the coordinates of point G.

Answer 1

To find the coordinates of point G, given the coordinates of point H (8, 7) and the midpoint of GH (7, 2), we used the midpoint formula. After solving a system of equations derived from the midpoint formula, we found that the coordinates of point G are (6, -3).

Step-by-step explanation:

To find the coordinates of point G when we know the coordinates of point H (8, 7) and the midpoint of segment GH (7, 2), we can use the midpoint formula which states that the midpoint M, with coordinates (xm, ym), of a segment with endpoints (x1, y1) and (x2, y2) can be found using:

xm = (x1 + x2) / 2

ym = (y1 + y2) / 2

We know that for point H, x1 = 8 and y1 = 7, and for the midpoint, xm = 7 and ym = 2. To find the coordinates of point G (x2, y2), we can set up the following system of equations:

7 = (8 + x2) / 2

2 = (7 + y2) / 2

By solving these equations, we can find the x and y coordinates of point G:

For x:

7 = (8 + x2) / 2

14 = 8 + x2

x2 = 14 - 8

x2 = 6

For y:

2 = (7 + y2) / 2

4 = 7 + y2

y2 = 4 - 7

y2 = -3

Therefore, the coordinates of point G are (6, -3).