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Question
Math
Posted 7 months ago

Point AA is at (2,4)(-2,4) and point BB is at (7,3)(7,3).
What is the midpoint of line segment AB\overline{A B} ?
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Answer from Sia
Verified answer
Posted 7 months ago
Solution by Steps
step 1
To find the midpoint of a line segment with endpoints (2,4)(-2, 4) and (7,3)(7, 3), we average the x-coordinates and the y-coordinates separately
step 2
The midpoint MM has coordinates (x1+x22,y1+y22)\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)
step 3
Substituting the given coordinates into the midpoint formula: M=(2+72,4+32)M = \left(\frac{-2 + 7}{2}, \frac{4 + 3}{2}\right)
step 4
Calculating the averages: M=(52,72)M = \left(\frac{5}{2}, \frac{7}{2}\right)
step 5
Converting the fractions to decimal form: M=(2.5,3.5)M = (2.5, 3.5)
[1] Answer
The midpoint of line segment AB\overline{AB} is (2.5,3.5)(2.5, 3.5).
Key Concept
Midpoint of a Line Segment
Explanation
The midpoint of a line segment with endpoints (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2) is found by averaging the x-coordinates and the y-coordinates separately to get the midpoint coordinates (x1+x22,y1+y22)\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right).

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