Ratios of Directed Line Segments
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What are the coordinates of the point on the directed line segment from $(- 7, - 5)$ to $(8, - 10)$ that partitions the segment into a ratio of 3 to 2 ?
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Answer

Combine the x and y coordinates to get the final answer: $(- 1, - 7)$

Steps

Step 1 ：Use the formula for dividing a line segment in a given ratio: $(x, y) = (\frac{x_{1} \cdot m + x_{2} \cdot n}{m + n}, \frac{y_{1} \cdot m + y_{2} \cdot n}{m + n})$

Step 2 ：Substitute the given values into the formula: $(- 7, - 5)$ and $(8, - 10)$ are the endpoints, and the ratio is 3 to 2

Step 3 ：Calculate the x-coordinate: $x = \frac{(- 7) \cdot 3 + 8 \cdot 2}{3 + 2} = \frac{- 21 + 16}{5} = \frac{- 5}{5} = - 1$

Step 4 ：Calculate the y-coordinate: $y = \frac{(- 5) \cdot 3 + (- 10) \cdot 2}{3 + 2} = \frac{- 15 - 20}{5} = \frac{- 35}{5} = - 7$

Step 5 ：Combine the x and y coordinates to get the final answer: $(- 1, - 7)$

Ratios of Directed Line SegmentsScore: 4/6 Penalty: 1 offQuestionWatch VideoShow ExamplesWhat are the coordinates of the point on the directed line segment from (−7,−5) to (8,−10) that partitions the segment into a ratio of 3 to 2 ?AnswerAttempt 2 out of 2

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Ratios of Directed Line Segments
Score: $4 / 6$ Penalty: 1 off
Question
Watch Video
Show Examples
What are the coordinates of the point on the directed line segment from $(- 7, - 5)$ to $(8, - 10)$ that partitions the segment into a ratio of 3 to 2 ?
Answer
Attempt 2 out of 2