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Math  /  Geometry

QuestionFind the midpoint of the line segment with the given endpoints. (2,8) and (4,6)(2,8) \text { and }(4,6)
The midpoint of the segment is . □\square (Type an ordered pair.)

Studdy Solution

STEP 1

1. The endpoints of the line segment are given as (2,8)(2, 8) and (4,6)(4, 6).
2. The midpoint formula for a line segment in a 2D Cartesian plane is applicable.

STEP 2

1. Recall the midpoint formula.
2. Substitute the given endpoint values into the formula.
3. Calculate the midpoint.

STEP 3

Recall the midpoint formula for a line segment with endpoints (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2):
M=(x1+x22,y1+y22) M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)

STEP 4

Substitute the given values (x1,y1)=(2,8)(x_1, y_1) = (2, 8) and (x2,y2)=(4,6)(x_2, y_2) = (4, 6) into the formula:
M=(2+42,8+62) M = \left( \frac{2 + 4}{2}, \frac{8 + 6}{2} \right)

STEP 5

Calculate the midpoint:
M=(62,142) M = \left( \frac{6}{2}, \frac{14}{2} \right) M=(3,7) M = (3, 7)
The midpoint of the segment is:
(3,7) \boxed{(3, 7)}

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