Problem

Use vector form to find the point that is \(1/5\) of the way from \((0,0)\) to \((10,5)\).

Neutral vector-partition reference: start (0, 0), end (10, 5), and fraction one-fifth from the start, without a vector, segment, or marked point.

Big Picture

What this problem is really about

Vector partition form keeps the starting point, direction, and fraction in one expression. We’ll write start plus the fraction times end minus start, compute the directed displacement, distribute the scalar to both components, add the scaled move to the start, and verify the remaining vector has the complementary scale.

Answer choices

Choose your path.

Preview only

(0, 0) + (1/5)⟨10, 5⟩ = (4, 1)

(0, 0) + (1/5)⟨10, 5⟩ = (2, 1)

(0, 0) + (1/2)⟨10, 5⟩ = (5, 2.5)

(0, 0) + (1/5)⟨10, 5⟩ = (10, 1)

The choices are visible. Checking your work and seeing which answer is correct happen inside Gozunta.

Use vector form to find the point that is \(1/5\) of the way from \((0,0)\) to \((10,5)\).

What this problem is really about

Turn the preview into practice.

Gozunta lets you study this problem—and more than 10,000 others.