Question

`stackrel(harr)(AB)` and `stackrel(harr)(BC)` form a right angle at point B. If A = (-3, -1) and B = (4, 4), what is the equation of `stackrel(harr)(BC)`

Answer 1

step 1

find the slope AB

A = (-3, -1) and B = (4, 4)

m=(y2-y1)/(x2-x1)------> m=(4+1)/(4+3)------> m=5/7

step 2

find the slope mBC

we know that

if two lines are perpendicular

then

the product of their slopes is equal to -1

so

mAB*mBC=-1-------> mBC=-1/mAB-----> -1/(5/7)-----> mBC=-7/5

step 3

with mBC and the point B = (4, 4) find the equation of the line BC

y-y1=m*(x-x1)-----> y-4=(-7/5)*(x-4)-----> y=-(7/5)*x+(28/5)+4---> y=-(7/5)*x+(48/5)

y=-1.4*x+9.6

therefore

the answer is

the equation of the line BC is

y=-1.4*x+9.6

see the attached figure