b Use the Pythagorean Theorem to find the length. Find the midpoints of the horizontal and vertical line segments between the points to find the midpoint.
To find the midpoint, we start by determining the distance between the points in the x and y-directions. Counting the number of units in both directions, we get 24 and 10.
This means that the midpoint of the horizontal line segment is 12 units to the right of D(-10,-4), half of the total x-distance. Similarly, the midpoint of the vertical line segment is 5 units below E(14,6).
We can begin by marking the points on a coordinate plane and counting the number of units in the x and y-direction.
The lengths of the vertical and horizontal line segments are 13 and 8 units. The midpoint of each segment will be 6.5 and 4 units from the endpoints.
This gives us the midpoint M(2.5,4).
Length
The line segment FG makes up the hypotenuse in a right triangle with legs 8 and 13 units long. Therefore, we use the Pythagorean Theorem to find the length.
