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What are the coordinates of the point on the directed line segment from (1,-5) to(10, 1) that partitions the segment into a ratio of 1 to 5?

 Feb 8, 2021
 #1
avatar+8435 
+1

Using the section formula directly,

 

The required point is \(\left(\dfrac{5(1) + 1(10)}{5 + 1}, \dfrac{5(-5) + 1(1)}{5 + 1}\right) = \left(\dfrac{5}{2}, -4\right)\)

 Feb 8, 2021
 #2
avatar+112447 
+2

Thanks Max,

 

I can never remember the formula so here is my method

I look at the x's and y's separately

 

x's

10-1=9

9/6=1.5

1+1.5=2.5

 

y's

1--5=6

6/6=1

-5+1=-4

 

(2,5,-4)

 Feb 8, 2021

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