Partitioning a Segment in a Ratio
Aligned to G-GPE.B.6 — Common Core State Standards for Mathematics.
What this lesson teaches
To find the point that divides a directed segment from A to B in the ratio m:n, move a fraction m/(m+n) of the way from A to B. The coordinates are A plus that fraction of the change in x and y. The midpoint is the special case with ratio 1:1.
Worked example
Find the point that partitions A(2, 3) to B(10, 11) in the ratio 1:3. The fraction from A is 1/(1+3) = 1/4. Change in x is 10 - 2 = 8; change in y is 11 - 3 = 8. Move 1/4 of each: x = 2 + (1/4)(8) = 2 + 2 = 4; y = 3 + (1/4)(8) = 3 + 2 = 5. The point is (4, 5).
Practice questions
- Find the midpoint of A(1, 2) and B(7, 10).
- Find the point 2/5 of the way from A(0, 0) to B(10, 15).
- Partition the segment from A(-4, 1) to B(8, 7) in the ratio 3:1.
Watch the lesson
Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.
▶ Watch this lessonEn español
Dividir un segmento en una razón
Para hallar el punto que divide un segmento dirigido de A a B en la razón m:n, avanza una fracción m/(m+n) del camino de A a B. Las coordenadas son A más esa fracción del cambio en x y en y. El punto medio es el caso especial con razón 1:1.
Ejemplo: Halla el punto que divide A(2, 3) a B(10, 11) en la razón 1:3. La fracción desde A es 1/(1+3) = 1/4. El cambio en x es 10 - 2 = 8; el cambio en y es 11 - 3 = 8. Avanza 1/4 de cada uno: x = 2 + (1/4)(8) = 2 + 2 = 4; y = 3 + (1/4)(8) = 3 + 2 = 5. El punto es (4, 5).
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