What you’ll learn
Partition a segment in a ratio.
Key idea
The fraction traveled from the first endpoint is first part divided by the sum of both parts.
Divide the first term by total parts, not the second term; add displacement to the first endpoint.
Worked example
Enter the exact value or ordered values in the format requested below.
P divides the segment A=(-2, -2) to B=(-12, 3) internally with AP:PB=2:3. Give P as an ordered pair.
- The whole-segment fraction is 2/(2+3)=2/5.
- P=A+2/5(B-A)=(-6,0).
Answer: (-6,0)
Quick Check
Evaluate a worked attempt at partition a segment in a ratio, identify the first invalid step, and provide the correction.
A=(-2, -2), B=(-6, 2) and AP:PB=3:1. Step 1 uses 3/1 of the whole displacement. Step 2 assigns P=(-14,10). Locate the first invalid step and correct P.