Problem

Interpret and compute this directed internal partition: start \(A=(0,0)\), end \(B=(9,6)\), internal ratio \(AP:PB=1:2\).

Neutral directed-partition reference: start A (0, 0), end B (9, 6), and ratio AP to PB 1 to 2, without a drawn segment or partition point.

Big Picture

What this problem is really about

Directed partitioning keeps both the endpoint order and the ratio order visible. We’ll translate the first ratio part into a fraction of the whole, subtract in the stated start-to-end direction, scale both displacement components, anchor the move at the correct start, and verify the ordered subsegment ratio.

Answer choices

Choose your path.

Preview only

P = (3, 2), and reversing the endpoints gives the same point.

P = (−3, −2), using A − B as the displacement.

P = (3, 2), because 1:2 places P one-third of the way from A to B.

P = (6, 4), because 1:2 places P two-thirds of the way from A to B.

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Interpret and compute this directed internal partition: start \(A=(0,0)\), end \(B=(9,6)\), internal ratio \(AP:PB=1:2\).

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