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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Warm-Up: Review What You Know

These problems review skills you have already learned.

What is the midpoint of the segment joining $(-3, 8)$ and $(7, -2)$ ?

$(2, 3)$ — average the two $x$ -coordinates and average the two $y$ -coordinates, since the middle point is halfway along in each direction.

$(5, -5)$ — find the change in $x$ and the change in $y$ across the segment, then halve each of those changes to land at the middle.

$(10, -10)$ — subtract the first point's coordinates from the second point's coordinates to get the change across the segment, then use that change as the midpoint.

$(4, 5)$ — add the coordinates of the two endpoints together, then halve only the $y$ -coordinate of that sum.