the-line-segment-joining-the-points-3-4-and-1-2-is-trisected-at-the-points-P-and-Q-if-the-coordinates-of-P-and-Q-are-p-2-and-5-3-q-respectively-find-the-values-of-p-and-q-

Question Number 24179 by gopikrishnan005@gmail.com last updated on 14/Nov/17

$${the}\:{line}\:{segment}\:{joining}\:{the}\:{points}\:\left(\mathrm{3},−\mathrm{4}\right)\:{and}\:\left(\mathrm{1},\mathrm{2}\right)\:{is}\:{trisected}\:{at}\:{the}\:{points}\:{P}\:{and}\:{Q}\:{if}\:{the}\:{coordinates}\:{of}\:{P}\:{and}\:{Q}\:{are}\:\left({p},−\mathrm{2}\right)\:{and}\:\left(\mathrm{5}/\mathrm{3},{q}\right)\:{respectively}\:{find}\:{the}\:{values}\:{of}\:{p}\:{and}\:{q}. \\ $$

Answered by mrW1 last updated on 14/Nov/17

$$\frac{{x}_{\mathrm{1}} −\mathrm{3}}{\mathrm{1}−\mathrm{3}}=\frac{\mathrm{1}}{\mathrm{3}} \\ $$$$\Rightarrow{x}_{\mathrm{1}} =\mathrm{3}−\frac{\mathrm{2}}{\mathrm{3}}=\frac{\mathrm{7}}{\mathrm{3}} \\ $$$$\frac{{y}_{\mathrm{1}} −\left(−\mathrm{4}\right)}{\mathrm{2}−\left(−\mathrm{4}\right)}=\frac{\mathrm{1}}{\mathrm{3}} \\ $$$$\Rightarrow{y}_{\mathrm{1}} =\mathrm{2}−\mathrm{4}=−\mathrm{2} \\ $$$$ \\ $$$$\frac{{x}_{\mathrm{2}} −\mathrm{1}}{\mathrm{3}−\mathrm{1}}=\frac{\mathrm{1}}{\mathrm{3}} \\ $$$$\Rightarrow{x}_{\mathrm{2}} =\mathrm{1}+\frac{\mathrm{2}}{\mathrm{3}}=\frac{\mathrm{5}}{\mathrm{3}} \\ $$$$\frac{{y}_{\mathrm{2}} −\mathrm{2}}{−\mathrm{4}−\mathrm{2}}=\frac{\mathrm{1}}{\mathrm{3}} \\ $$$$\Rightarrow{y}_{\mathrm{2}} =\mathrm{2}−\mathrm{2}=\mathrm{0} \\ $$$$ \\ $$$$\Rightarrow{p}=\frac{\mathrm{7}}{\mathrm{3}} \\ $$$$\Rightarrow{q}=\mathrm{0} \\ $$

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