Question

The endpoints of a line segment are G(1, 7) and H(-3, 11). Find the coordinates of the midpoint M. Find the distance between the endpoints of GH.

Answer 1

The coordinates of the midpoint M are (-1, 9). The distance between the endpoints of GH is 4 units.

Step-by-step explanation:

To find the coordinates of the midpoint M, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint between two points (x1, y1) and (x2, y2) are given by:

Midpoint(x,y) = ((x1 + x2)/2, (y1 + y2)/2)

In this case, the coordinates of point G are (1, 7) and the coordinates of point H are (-3, 11). Plugging these values into the formula, we get:

Midpoint(x,y) = ((1 + (-3))/2, (7 + 11)/2)

Simplifying, we find that the coordinates of the midpoint M are (-1, 9).

To find the distance between the endpoints of GH, we can use the distance formula. The distance formula states that the distance between two points (x1, y1) and (x2, y2) is given by:

Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Using the coordinates of G and H, we have:

Distance = sqrt((-3 - 1)^2 + (11 - 7)^2)

Simplifying, we find that the distance between the endpoints of GH is 4 units.