In what ratio does the point $$\left( \frac{24}{11},\,y \right)$$ divides the line segment joining the points P (2, –2) and Q (3, 7) ? Also find the value of y?

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Vedantu Content Team · Accepted Answer

Hint: To find the ratio and the value of y, we have to assume that the line segment PQ is in the ratio of $$\left( \lambda :1 \right)$$Complete step by step solution: It is given:Point $$B\left( \frac{24}{11},\,y \right),\,P(2,-2),\,Q(3,7)$$So, $$\begin{align}  & {{x}_{1}}=2,\,{{y}_{1}}=-2 \  & {{x}_{2}}=3,\,{{y}_{2}}=7 \ \end{align}$$According to the assumption, we can say that$$\left( x=\frac{\lambda {{x}_{2}}+{{x}_{1}}}{\lambda +1} \right)$$		....(1)$$\left( y=\frac{\lambda {{y}_{2}}+{{y}_{1}}}{\lambda +1} \right)$$		....(2)By putting values and solving the equation (1), we get$$\begin{align}  & \frac{24}{11}=\frac{\lambda (3)+2}{\lambda +1} \  & 24\lambda +24=33\lambda +22 \  & \lambda =\frac{2}{9} \ \end{align}$$By putting values and solving the equation (2), we getSo, the ratio in which B divides PQ =2:9 and the value of y=-(4/11)$$\begin{align}  & y=\frac{(2/9\times 7)+(-2)}{(2/9+1)} \  & y=\frac{(14/9)-2}{(11/9)} \  & y =-\frac{4}{11} \ \end{align}$$.Note: Values should be put correctly. Before putting values, it is important to identify the values of $${{x}_{1}},\,{{x}_{2}},\,{{y}_{1}}\,and\,{{y}_{2}}$$.

In what ratio does the point \[\left( \frac{24}{11},\,y \right)\] divides the line segment joining the points
P (2, –2) and Q (3, 7) ? Also find the value of y?

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In what ratio does the point \[\left( \frac{24}{11},\,y \right)\] divides the line segment joining the points P (2, –2) and Q (3, 7) ? Also find the value of y?

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