Question

Point P(-4, 6) divides the segment joining points A(-6, 10) and B(r, s) in the ratio 2:1 . Find the coordinates of the point B​

Answer 1

Step-by-step explanation:

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Class 10>>Maths>>Coordinate Geometry>>Section Formula>>If point ( - 4,6) divides the line seqme

Question

If point (-4,6) divides the line seqment AB with A (-6,10) & B (r,s) in the ratio 2 : 1,  then find r and s

Using the section formula, if a point (x,y) divides the line joining the points (x1,y1) and (x2,y2) in the ratio m:n, then 

(x,y)=(m+nmx2+nx1,m+nmy2+ny1)

& for mid points we have, m:n=1:1.

Therefore, we have

(−4,6)=(2+12r−6,2+125+10)

⇒32r−6=−4

325+10=6

⇒2r−6=−12,25+10=18

Answer 2

The coordinates of the point $B$ are $(-3,4)$.

Tips:

If $A$ point $P\:(x,y)$ divides the line segment joining the points $A\:(x_{1},y_{1})$ and $B(x_{2},y_{2})$ into the ratio $m:n$, then

$x=\dfrac{nx_{1}+mx_{2}}{m+n}$ and

$y=\dfrac{ny_{1}+my_{2}}{m+n}$

Step-by-step explanation:

Using the above formula, we have

$-4=\dfrac{1(-6)+2(r)}{2+1}$

$\Rightarrow -4=\dfrac{-6+2r}{3}$

$\Rightarrow -6+2r=-12$

$\Rightarrow 2r=-6$

$\Rightarrow r=-3$

and $6=\dfrac{1(10)+2(s)}{2+1}$

$\Rightarrow 6=\dfrac{10+2s}{3}$

$\Rightarrow 2s+10=18$

$\Rightarrow 2s=8$

$\Rightarrow s=4$

∴ the coordinates of $B$ are $(-3,4)$.

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