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Math  /  Geometry

QuestionDistance and Midpoint
Find the midpoint for the segment with endpoints of (−2,0)(-2,0) and (4,−6)(4,-6). (2,−1)(2,-1) (2,−4)(2,-4) (1,−4)(1,-4) (2,−3)(2,-3) (1,−3)(1,-3)

Studdy Solution

STEP 1

1. The segment has endpoints at (−2,0)(-2, 0) and (4,−6) (4, -6) .
2. The formula for the midpoint of a segment is known.

STEP 2

1. Recall the formula for the midpoint of a segment.
2. Substitute the given endpoints into the formula.
3. Calculate the midpoint.

STEP 3

Recall the formula for the midpoint of a 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 endpoints (−2,0)(-2, 0) and (4,−6) (4, -6) into the formula:
M=(−2+42,0+(−6)2) M = \left( \frac{-2 + 4}{2}, \frac{0 + (-6)}{2} \right)

STEP 5

Calculate the midpoint:
M=(−2+42,0−62) M = \left( \frac{-2 + 4}{2}, \frac{0 - 6}{2} \right) M=(22,−62) M = \left( \frac{2}{2}, \frac{-6}{2} \right) M=(1,−3) M = (1, -3)
The midpoint of the segment is:
(1,−3) \boxed{(1, -3)}

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