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Find the sum of all values of a such that the point (a,21) is 10 sqare root 2 from the point (4,7).

 Feb 21, 2020
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Find the sum of all values of a such that the point (a,21) is 10 sqare root 2 from the point (4,7).

 

Finden Sie die Summe aller Werte von a so, dass der Punkt (a, 21) \(10\cdot \sqrt{2}\) )  vom Punkt (4,7) entfernt ist.

 

\(x_1=a\\ x_2=4\\ y_1=21\\ y_2=7\)

 

\(y=\frac{y_2-y_1}{x_2-x_1}(x-x_1)+y_1 \)

 

\((x_2-a)^2+(y_2-y_1)^2=(10\cdot \sqrt{2})^2\\ (4-a)^2+(7-21)^2=(10\cdot \sqrt{2})^2\\ 16-8a+a^2+196=200\)

\(a^2-8a+12=0\\ a=4\pm\sqrt{16-12}=4\pm 2 \)

\(a_1=6\\a_2=2\\ \sum{(a_{values})}=8\)

laugh  !

 Feb 22, 2020
edited by asinus  Feb 22, 2020

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