Question

M(12, 1) is the midpoint of DG. If D is at (6, 5), then where is G?

Answer 1

The coordinates for point G can be found using the midpoint formula by plugging in the midpoint M(12, 1) and one endpoint D(6, 5), resulting in G(18, -3).

Step-by-step explanation:

You have a midpoint M at coordinates (12, 1) for the line segment DG. The coordinates for point D are given as (6, 5). To find the coordinates for point G, you can use the midpoint formula which states that the midpoint's coordinates are the averages of the x and y coordinates of the endpoints. The formulas are as follows:

Midpoint x-coordinate = ( x1 + x2 ) / 2

Midpoint y-coordinate = ( y1 + y2 ) / 2

Plugging in the known values for the midpoint and point D, and solving for point G:

• 12 = (6 + x2) / 2
• 1 = (5 + y2) / 2

Solving these equations gives us:

• x2 = 12 * 2 - 6 = 24 - 6 = 18
• y2 = 1 * 2 - 5 = 2 - 5 = -3

So the coordinates for point G are (18, -3).