Question

Find the value of k if P(4,-2 ) is the mid point of hte line segment joining the points A(5k, 3) and B(-k, 7)

Answer 1

mid point formula
(a,b)=coordinates of the midpoint of line joining two points (5k,3) and (-k,7)
(a,b)=(5k-k/2,7+3/2)
therefore 4k/2=a
given a =4
2k=4
k=2

Answer 2

Answer:

The value of k = 2

Step-by-step explanation:

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we know that,

The midpoint of the line segment joining $A(x_{1},y_{1}) \\\: and \: B(x_{2},y_{2}) \: is \:\\ \left( \frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2}\right)$

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Now , Here given

P(4,-2) is the midpoint of the line segment joining the points

$A(x_{1},y_{1})=(5k,3)\: and \\\: B(x_{2},y_{2})=(-k,-7)$

$\left(\frac{5k+(-k)}{2},\frac{3+(-7)}{2}\right)=P(4,-2)$

$\implies \left(\frac{5k-k}{2},\frac{3-7}{2}\right)=P(4,-2)$

$\implies \left(\frac{4k}{2},\frac{-4}{2}\right)=P(4,-2)$

$\implies \left(2k,-2\right)=P(4,-2)$

$\implies 2k=4$

/* we know that ,

If (a,b) = (c,d) then a=c and b=d */

$\implies k= \frac{4}{2}$

Therefore,

The value of $ k = 2 $

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