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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Fluency Practice

Point $P$ partitions the directed segment from $C(1, -5)$ to $D(11, 10)$ in the ratio $2:3$ . What are the coordinates of $P$ ?

$(7, 4)$ — weight $C$ by $2$ and $D$ by $3$ , matching the first ratio number to the first point named in the problem.

$\left(\frac{23}{3}, 5\right)$ — move $\frac{2}{3}$ of the way from $C$ toward $D$ , reading the two ratio numbers as a numerator and a denominator.

$\left(6, \frac{5}{2}\right)$ — take the midpoint of the segment, since $2$ and $3$ are close enough in size that the point lands near the center.

$(5, 1)$ — move $\frac{2}{5}$ of the way from $C$ toward $D$ , since $2 + 3 = 5$ equal parts make up the whole segment.