Question

AB and BC form a right angle at their point of intersection, B.

Answer 1

To find the y intercept of AB, first find the slope of AB: m=(1-(-1))/(2-14)=-1/6
the equation of line AB is y=-(1/6)x+b
use either of the given two points to find out b: 1=(-1/6)*2+b => b=4/3
BC is perpendicular to AB, so the slope of BC is the negative reciprocal of the slope of AB, therefore, the slope of BC is 6
Equation of BC is y=6x+b
find out b by using the coordinates of point B: 1=6*2+b  => b=-11
the equation of BC is: y=6x-11

the x coordinate of point C: 13=6*x -11 =>x=4

Please double check my calculation.