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# Ratios

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1. Given the directed line segment from A to B, construct a point P that dives the segment ratio 5 to 2 from A to B.

2. Find the point P along the directed line segment from point A (-14, 2) to point B (0,15) that divides the segment in the ratio 1 to 4.

I've tried both but I don't understand ratios and the points. The first one doesn't even have any points so I don't know how I'm supposed to solve it. Please help.

May 8, 2019

#1
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Well.....for the first one......we can let A  = (0,0)   and B  = (7,0)

So.....if we let P  = (5, 0)......the distance from A to P  = 5

And the distance from P to B  = 2

So.....the segment is diveded in a ratio of   AP : PB  =   5 : 2   May 8, 2019
#2
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2. Find the point P along the directed line segment from point A (-14, 2) to point B (0,15) that divides the segment in the ratio 1 to 4.

If we have a ratio of  1 : 4......there are 5 equal parts of the segment

So   AP  =  1/5 of the distance from A to B     and PB  = 4/5  of the distance from A to B

Here's the way to find P

( x coordinate of A + (1/5) (x coordinate of B - x coordinate of A)  =

[ -14 + (1/5) ( 0 - - 14 ]   =    [ -14 + (1/5)(14) ]  =  [ -14 + 14/5 ]  =  [ =70/5 + 14/5 ] = [ -56/5 ]

This is the x coordinate of P

To find the y coordinate of P, we use the same idea

( y coordinate of A + (4/5)(y coordinate of B - y coordinate of A) )  =

[ 2 + (4/5) (15 - 2) ] =  [ 2 + (4/5)(3) ]  = [ 2 + 12/5]  =  [ 22/5]

This is the y coordinate of P

So  P  =   ( -56/5, 22/5)

See this graph :  https://www.desmos.com/calculator/tn3bp9xvf6   May 8, 2019