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In what ratio does the points p (2,-5) divide the line segment joining A(-3,5) and B(4 ,- 9)

Posted by Sahana Sahana 1 year, 8 months ago

CBSE > Class 10 > Mathematics

2 answers

Preeti Dabral 1 year, 8 months ago

Let the required ratio be k:1.
Then, by the section formula, the coordinates of P are
{tex}P \left( \frac { 4 k - 3 } { k + 1 } , \frac { - 9 k + 5 } { k + 1 } \right){/tex}
{tex}\therefore \quad \frac { 4 k - 3 } { k + 1 } = 2 \text { and } \frac { - 9 k + 5 } { k + 1 } = - 5{/tex} [{tex}\because{/tex} P(2, 5) is given]
{tex}\Rightarrow{/tex} 4k - 3 = 2k + 2 and -9k + 5 = -5k - 5
{tex}\Rightarrow{/tex} 2k = 5 and 4k = 10
{tex}\Rightarrow{/tex} {tex}k = \frac { 5 } { 2 }{/tex} in each case.
So, the required ratio is {tex}\frac { 5 } { 2 } : 1, {/tex} which is 5:2
Hence, P divides AB in the ratio 5:2.

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Ashitha Saran 1 year, 8 months ago

A=(x1,y1)=(−3,5) and B=(x2,y2)=(4,−9) Let us assume that R(x,y)=(2,−5) divides AB in the ratio m:n, then using section formula: x=m+nmx2+nx1 2=m+n4m+(−3)n 2m−5n=0…(1) And, y=m+nmy2+ny1 −5=m+n−9m+5n 2m−5n=0…(2) In both the cases, we have: 2m=5n nm=25 ∴m:n=5:2

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