Back to Find point partitioning segment — Problem 3 · Task Set 35

Exercises: Find the Point Partitioning a Directed Line Segment

Show your work for each problem. Unless a problem says otherwise, a ratio $m:n$ always describes the directed segment read from the first named point to the second. Give coordinates as exact values, using fractions rather than rounded decimals.

Grade 10·25 problems·~35 min·Common Core Math - HS Geometry·standard·hsg-gpe-b-6

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Warm-Up: Review What You Know

These problems review skills you have already learned.

Two triangles are similar with a scale factor of $\frac{2}{5}$ from the larger to the smaller. The larger triangle has a horizontal leg of length $20$ . How long is the corresponding horizontal leg of the smaller triangle?

$50$ — multiply the known leg by $\frac{5}{2}$ , using the scale factor upside down so the matching side comes out longer than the one you started from.

$8$ — multiply the known leg by the scale factor, since corresponding sides of similar figures are related by that constant multiplier.

$18$ — subtract the difference between the two numbers in the scale factor, treating $5 - 2 = 3$ as an amount to remove from the leg length.

$10$ — halve the known leg, reading the scale factor $\frac{2}{5}$ as though it meant "cut in half twice as evenly."