If the point(x,14)divides the line joining the points (7,11) and (-18,16),find the value of x?

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Answer 1 · 2018-06-21T20:17:10

#x = -8#

#A = ((7), (11)) ; B = ((-18), (16)); C = ((x), (14))#

#B - A = ((-25), (5))#

#C = A + lambda (B - A)#

#((x), (14)) = ((7), (11)) + lambda ((-25), (5))#

#14 = 11 + 5 lambda => lambda = 3/5#

#x = 7 - 3/5 * 25#

Answer 2 · 2018-06-21T20:29:42

#color(blue)(x=-8)#

If a point P divides a line segment AB in a given ratio #m:n#, the the co-ordinates of the point P are given by:

#x=x_1+m/(m+n)(x_2-x_1)#

#y=y_1+m/(m+n)(y_2-y_1)#

This is known as the section formula

For y we have:

#y=14#

#:.#

#14=11+m/(m+n)(16-11)#

#3=m/(m+n)(5)#

#m/(m+n)=3/5#

For x:

#x=7+3/5(-18-7)#

#x=-8#

So, co-ordinates of point P are:

#(-8,14)#

#m/(m+n)=3/5=>m=3 and n=2#

The line has been divided in a #3:2# ratio.

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