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Math  /  Geometry

QuestionFind the midpoint of the line segment with the given endpoints. (−6,−3) and (−1,−5)(-6,-3) \text { and }(-1,-5)
The midpoint is □\square (Type an ordered pair.)

Studdy Solution

STEP 1

1. The endpoints of the line segment are given as (−6,−3)(-6, -3) and (−1,−5)(-1, -5).
2. The midpoint formula for a line segment in a 2D 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 endpoint values (−6,−3)(-6, -3) and (−1,−5)(-1, -5) into the formula:
M=(−6+(−1)2,−3+(−5)2) M = \left( \frac{-6 + (-1)}{2}, \frac{-3 + (-5)}{2} \right)

STEP 5

Calculate the midpoint:
M=(−6+(−1)2,−3+(−5)2) M = \left( \frac{-6 + (-1)}{2}, \frac{-3 + (-5)}{2} \right) =(−72,−82) = \left( \frac{-7}{2}, \frac{-8}{2} \right) =(−72,−4) = \left( -\frac{7}{2}, -4 \right)
The midpoint of the line segment is:
(−72,−4) \boxed{\left( -\frac{7}{2}, -4 \right)}

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