AB and BC form a right angle at their point of intersection. This means AB is perpendicular to BC.
We are given the coordinates of points A and B, using which we can find the equation of the line for AB.
Slope of AB will be:
[tex]m= \frac{-1-1}{14-2}=-1/6 [/tex]
Using this slope and the point (2,1) we can write the equation for AB as:
[tex]y-1= \frac{-1}{6}(x-2) \\ \\
y= -\frac{1}{6}x+ \frac{1}{3}+1 \\ \\
y=-\frac{1}{6}x+ \frac{4}{3}
[/tex]
The above equation is in slope intercept form. Thus the y-intercept of AB is 4/3.
Slope of AB is -1/6, so slope of BC would be 6. Using the slope 6 and coordinates of the point B, we can write the equation of BC as:
y - 1 = 6(x - 2)
y = 6x - 12 + 1
y = 6x - 11
Point C lies on the line y = 6x - 11. So if the y-coordinate of C is 13, we can write:
13 = 6x - 11
24 = 6x
x = 4
The x-coordinate of point C will be 4.
Therefore, the answers in correct order are:
4/3 , 6, -11, 4
