Question and Answers Forum

All Questions      Topic List

Others Questions

Previous in All Question      Next in All Question      

Previous in Others      Next in Others      

Question Number 32834 by Rio Mike last updated on 03/Apr/18

find  the value of k for which the   length of the line segment joining  (k^� ,2) and (−1,4) is 2(√2) units.      show full working...

$${find}\:\:{the}\:{value}\:{of}\:{k}\:{for}\:{which}\:{the}\: \\ $$$${length}\:{of}\:{the}\:{line}\:{segment}\:{joining} \\ $$$$\left(\bar {{k}},\mathrm{2}\right)\:{and}\:\left(−\mathrm{1},\mathrm{4}\right)\:{is}\:\mathrm{2}\sqrt{\mathrm{2}}\:{units}. \\ $$$$\:\:\:\:{show}\:{full}\:{working}... \\ $$

Answered by MJS last updated on 03/Apr/18

(√((k+1)^2 +(2−4)^2 ))=2(√2)  (√(k^2 +2k+5))=2(√2)  k^2 +2k+5=8  k^2 +2k−3=0  k=−1±(√(1+3))=−1±2  k_1 =−3  k_2 =1

$$\sqrt{\left({k}+\mathrm{1}\right)^{\mathrm{2}} +\left(\mathrm{2}−\mathrm{4}\right)^{\mathrm{2}} }=\mathrm{2}\sqrt{\mathrm{2}} \\ $$$$\sqrt{{k}^{\mathrm{2}} +\mathrm{2}{k}+\mathrm{5}}=\mathrm{2}\sqrt{\mathrm{2}} \\ $$$${k}^{\mathrm{2}} +\mathrm{2}{k}+\mathrm{5}=\mathrm{8} \\ $$$${k}^{\mathrm{2}} +\mathrm{2}{k}−\mathrm{3}=\mathrm{0} \\ $$$${k}=−\mathrm{1}\pm\sqrt{\mathrm{1}+\mathrm{3}}=−\mathrm{1}\pm\mathrm{2} \\ $$$${k}_{\mathrm{1}} =−\mathrm{3} \\ $$$${k}_{\mathrm{2}} =\mathrm{1} \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com