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.

Guest May 8, 2019

#1**+1 **

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

CPhill May 8, 2019

#2**+1 **

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

CPhill May 8, 2019