Find the sum of all values of a such that the point (a,21) is 10 sqare root 2 from the point (4,7).
+14913 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.
\(x_1=a\\ x_2=4\\ y_1=21\\ y_2=7\)
\(y=\frac{y_2-y_1}{x_2-x_1}(x-x_1)+y_1 \)
\((x_2-a)^2+(y_2-y_1)^2=(10\cdot \sqrt{2})^2\\ (4-a)^2+(7-21)^2=(10\cdot \sqrt{2})^2\\ 16-8a+a^2+196=200\)
\(a^2-8a+12=0\\ a=4\pm\sqrt{16-12}=4\pm 2 \)
\(a_1=6\\a_2=2\\ \sum{(a_{values})}=8\)
!
