Back to Find point partitioning segment — Problem 1 · 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

Which point partitions the directed segment from $A(2, 1)$ to $B(10, 9)$ in the ratio $1:3$ ?

$(6, 5)$ — split the segment evenly, since a ratio with a $1$ in it marks off one equal share on each side of the point.

$\left(\frac{14}{3}, \frac{11}{3}\right)$ — travel $\frac{1}{3}$ of the way from $A$ toward $B$ , reading the ratio $1:3$ directly as the fraction one-third.

$(4, 3)$ — travel $\frac{1}{4}$ of the way from $A$ toward $B$ , since the ratio $1:3$ divides the segment into $1 + 3 = 4$ equal parts.

$(8, 7)$ — weight $A$ by $1$ and $B$ by $3$ , putting the first ratio number on the starting point and the second on the ending point.