Points and Distance

Partition Segment

Use a fraction of the total change in x and y to divide a segment in a given ratio.

partition-segment P = A + (m/(m+n))(B-A)

Example

Use a ratio to locate a point along a segment.

highlighted = computed this step

Step 1 — Plot partition point

Plot A, B, and partition point P.

Coordinate plot\text{Coordinate plot}
Partition segment plotSegment from A(2, 1) to B(8, 7) with partition point P(4, 3).ABP

Step 2 — Ratio fraction

Turn the ratio into a fraction of the segment.

t=1/(1+2)=13t= 1 /( 1 + 2 )= \hlmath{\frac{1}{3}}

Step 3 — Partition x-coordinate

Move that fraction in the x-direction.

x=2+13⋅(8−2)=4x= 2 + \frac{1}{3} \cdot( 8 - 2 )= \hl{4}

Step 4 — Partition y-coordinate

Move that fraction in the y-direction.

y=1+13⋅(7−1)=3y= 1 + \frac{1}{3} \cdot( 7 - 1 )= \hl{3}

Step 5 — Partition point

State the partition point.

P=(4,3)P=( \hl{4} , \hl{3} )