Find the point that divides the segment from (-4,-3) to (5,3) in the ratio 5:3.

 May 31, 2020

To solve this problem, I went to Youtube. If you want to follow along and do it, here's the link to the video I used, but if you want an explanation without watching a video, I will do my best to explain below. 


Plot the points given. I labeled them KL in the graph below.




As you can see, I have made a lot of side notes. It may be hard to understand at first, but bare with me.

I drew a straight line across from K, and then a straight line down from L, connecting the both into a triangle.


The point I labeled at (?,?) is the point we're trying to find. It's only an APPROXIMATE spot!!!! This is just a visual for your understanding.

To divide the segment into the 5:3 ratio, we must conclude that there's some point that divides x into the ratio 5:3 and there's some point that divides y into the ratio 5:3. (I represented this by putting 5x and 3x, and 5y and 3y.)


Then, we need to think about what the total change in x is from point K (-4, -3) to point L (5, 3). Doing this, we find the distance between the x on each point. So ask yourself what the distance is from -4 to 5.
It is going to be 9. (I represented this on the image, where delta = 9)


Next, we do the same for the distance between y on each point. Ask yourself what the distance is from -3 to 3.
It's going to be 6. (I also represented this on the image too, where delta = 6.)




Now that you understand everything on the graph, you can use the information given to find the point that divides the segment from each point.

Form two equations with x and y from the graph, and then solve. This is not the last step yet, sadly. 


5x + 3x = 9 

8x = 9

x = 9/8


3y + 5y = 6

8y = 6

y = 6/8

y = 3/4


Using the point (-4, -3), we can use the x and y values to finally determine the point that divides the segment from each point.


Let's label (?,?) as P. 


P ( -4 + (5 x (9/8)), -3 + (5 x (3/4)) )

Solve for for point P.


P ( -4 + (5 x (9/8)), -3 + (5 x (3/4)) )

P ( -4 + 5.525, -3 + 3.75 )

P ( 1.625, 0.75 ) 
OR you can flip it into a fraction.

P ( 13/8 , 3/4 )


The point that divides the segment from each point can be represented at ( 13/8 , 3/4 ).

 May 31, 2020

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