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# coordinates

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Find the ratio in which the point P(11, y) divides the line segment joining the points A(15,5) and B(9, 20). Also, find the value of y.​

Jun 13, 2022

#1
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Use section formula (x,y)=(mx2+nx1/m+n,my2+ny1/m+n) in which m:n are the ratio and (x1,y1) and (x2,y2)

are the points.

Let k:1

Substituting the values from the points mentioned above to (mx2+nx1/m+n,my2+ny1/m+n) gives

(11,y)=(9k+15 / k+1,20k+5 / k+1)

Equate first component to get ratio:

​9k+15 / k+1=11

9k+15=11k+11

2k=4k

k=2

22:1​

Do the same for the second to get the value for y:

Calculation:

​y=20×2+5 / 2+1

=45/3

y=15​

-Vinculum

Jun 13, 2022
#2
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Write the equation of the line between  (15, 5)  and ( 9, 20)

Slope = (20 - 5) / ( 9 - 15) =  15 / - 6 =   -5/2

y =  -(5/2)(x - 9)  + 20

y =  (-5/2)x + 45/2 + 20

y =  ( -5/2)x + 85/2

When x =  11

y = (-5/2)(11) + 85/2  =  30 / 2  =  15

Let C = (11,15)

The ratio  is

AC  /   BC

sqrt [ (15 - 11)^2 + (5-15)^2 ]                   sqrt  [ 116]

_________________________   =        __________  = sqrt (116 / 29) =  sqrt (4) / 1  =   2  :  1

sqrt [ ( 9 - 11)^2 + ( 20 - 15)^2 ]               sqrt [  29 ]   Jun 13, 2022