Midpoints
Midpoint on a Number Line
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Midpoint – the point in the in the middle of a line segment
Bisector – a point, line, or line segment that creates a division of a geometric object into two congruent parts
A line has no endpoints and no midpoint
Line segments have midpoints at the average of the endpoint coordinates
Midpoint in the Coordinate Plane
• Endpoints have both an x- and y-value in a two dimensional coordinate plane
• Midpoint formula – the formula connecting the coordinates of the midpoint with the coordinates of the
endpoints
The midpoint formula
Given points 𝐴(𝑥! , 𝑦! ) and 𝐵(𝑥! , 𝑦! ),
!
!! !!! !! !!!
!
,
!
!
!!!! .
is the midpoint of the line segment 𝐴𝐵
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Algebra I 3.2 Midpoints
Midpoints
Derivation of the Midpoint Formula
• The midpoint is the location halfway from A to B along 𝐴𝐵
• To find the midpoint of a segment on a coordinate plane
• Step 1 | Average of horizontal components for the x! !!
coordinate, ! !
!
• Step 2 | Average of the vertical components for the y! !!
coordinate, ! !
!
• Step 3 | Write the two averages as a point (x,y)
Fractional Distance
• Fractional distance – the length of a designated portion of a line
segment
• Fractional distance in the coordinate plane requires computing xand y-coordinates separately
• Ex) One-third the distance from P and Q is four units
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Algebra I 3.2 Midpoints