+0  
 
0
279
1
avatar+406 

 

8) What are the coordinates of the midpoint of the line segment with endpoints D(-5, 3)  E(2, -2)?

 

 

 

 

9) Point A is located at (3, 2 ) and point B is located at ( 10, 12). What are the coordinates of the point that partitions the directed line segment in a 3: 2   ratio?

 

 

 

 

 

10) Point A is located at (1, 2) and point B is located at ( 13, 8). What are the coordinates of the point that partitions the directed line segment in a 5: 1   ratio?

 Feb 19, 2018
 #1
avatar+7347 
+3

8)

We can think of this as the point that divides the line segment in a 1:1 ratio.

 

x-coordinate   =   -5 + 1/(1 + 1) * (2 - -5)   =   -5 + 1/2 * 7   =   -5 + 7/2   =   -1.5

y-coordinate   =    3 - 1/(1 + 1) * (3 - -2)   =    3 - 1/2 * 5   =    3 - 5/2   =   0.5

 

The coordinates are  (-1.5, 5.5)

Here's a graph:   https://www.desmos.com/calculator/m4soc58v9b

 

9)

 

x-coordinate   =   3 + 3/(3 + 2) * (10 - 3)   =   3 + 3/5 * 7   =   3 + 21/5   =   7.2

y-coordinate   =   2 + 3/(3 + 2) * (12 - 2)   =   2 + 3/5 * 10   =   2 + 30/5   =   8

 

The coordinates are  (7.2, 8)

 

Here's a graph:   https://www.desmos.com/calculator/sravdf6fly

I changed the step size and shifted all the points to the left so that you can see that (7.2, 8) is three-fifths from point A in the x and y direction.

 

10)

 

x-coordinate   =   1 + 5/(5 + 1) * (13 - 1)   =   1 + 5/6 * 12   =   1 + 60/6   =   11

y-coordinate   =   2 + 5/(5 + 1) * ( 8 - 2 )   =   2 + 5/6 * 6   =   2 + 5   =   7

 

The coordinates are  (11, 7)

 

Here's a graph:   https://www.desmos.com/calculator/goetjvhgit

 Feb 19, 2018

11 Online Users

avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.