What we need to do first, is to write the equation of the line through points A and B.
the slope of the line through A(3, 7) and B(-4, 9) is
[tex]m= \frac{9-7}{-4-3}= \frac{2}{-7}=- \frac{2}{7} [/tex]
the equation of the line is :
[tex]y-7=- \frac{2}{7}(x-3)\\\\y-7=- \frac{2}{7}x+ \frac{6}{7}\\\\y= - \frac{2}{7}x+ \frac{6}{7}+ \frac{49}{7}\\\\y= - \frac{2}{7}x+ \frac{55}{7} [/tex]
C(a, 1) is on this line so it must satisfy the equation:
[tex]y= - \frac{2}{7}x+ \frac{55}{7} \\\\1= - \frac{2}{7}a+ \frac{55}{7}\\\\ \frac{2}{7}a= \frac{48}{7}\\\\2a=48\\\\a=24 [/tex]
