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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