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.
+579 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
+128475 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 ]
