AnswersCR CCSS Math 2 S2 M2960OXDirected Line Segments and ModelingQuestion 112811
112811
AssignmentMultiple Choice

Directed Line Segments and Modeling

Question 112811 • *CR CCSS Math 2 S2 [M2960OX]

In the coordinate plane, the directed line segment from K to N has endpoints at K(–6, –2) and N(8, 3). Point L partitions the directed line segment from K to N in a ratio of 1:2. Point M partitions the directed line segment from L to N in a ratio of 3:1. What are the coordinates of point M? Round to the nearest tenth, if necessary.

Answer
A
(–1.3, –0.3)
B
(2.5, 1)
C
(5.7, 2.2)
D
(7, 2.5)

Explanation

Since KL:LN = 1:2, point L is one-third of the way from K to N. The change from K to N is (14, 5), so L = (−6 + 14/3, −2 + 5/3) ≈ (−1.3, −0.3). Since LM:MN = 3:1, M is three-fourths of the way from L to N, giving M ≈ (5.7, 2.2), choice C.

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