If the middle point of the line segment joining (3,4) and (k,7) is (x,y) and 2x+2y+1=0, find the value of k.
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Answer:
Value \:of \: k = -15
Step-by-step explanation:
The \: midpoint \: of \: line \: joining \\two \: points \: (x_{1},y_{1}) \:and \: (x_{2},y_{2})\:is \\\left(\frac{x_{1}+x_{2}}{2},\frac{x_{1}+x_{2}}{2}\right)
The \: midpoint \: of \: line \: joining \\two \: points \: (3,4) \:and \: (k,7)=(X,Y)\:(given)
\implies \left(\frac{3+k}{2},\frac{4+7}{2}\right)=(X,Y)
\implies \left(\frac{3+k}{2},\frac{11}{2}\right)=(X,Y)
\implies \frac{3+k}{2}=X\:---(1) \\ \: \frac{11}{2}=Y\:---(2)
But , \: 2X + 2Y + 1 = 0 \: (given)
\implies 2\times \frac{3+k}{2}+2\times \frac{11}{2}+1=0\\[From \:(1)\:and\: (2)]
\implies 3+k+11+1=0
\implies k + 15 = 0
\implies k = -15
Therefore,
Value \:of \: k = -15
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