Find the equation of Line BC, which is perpendicular to Line AB and runs through Point B.

Question

Line AB runs through the following points: A: (2,3)B: (4,7)

Find the equation of Line BC, which is perpendicular to Line AB and runs through Point B.

Answer 1

Given points are A(2, 3) and (4, 7)

Let (x1, y1) = (2, 3) and (x2, y2) = (4, 7)

Two Points Form of a Line Equation is (y - y1)  =  [ (y2 - y1) / (x2 - x1) ] (x - x1)

Substitute(x1, y1) = (2, 3) and (x2, y2) = (4, 7)

(y - 3)  =  [ (7 - 3) / (4 - 2)] (x - 2)

(y - 3)  =  [ 4 / 2] (x - 2)

2(y - 3)  =  4(x - 2)

2y - 6  =  4x - 8

2y  =  4x - 8 + 6

2y  =  4x - 2

y  =  (4x - 2) / 2

y  =  (4x)/2 - (2)/2

y  =  2x - 1 --------------------> (1)

Compare Eq (1) with point slope form y = mx + c

Slope m = 2.

If two lines are perpendicular to each other then 

m1 X m2  =  -1

2 X m2  =  -1

m2  =  -1/2

Point slope form of a line equation is y - y1  =  m (x - x1) -----------> (2)

Substitute m = -1/2 and point B (x1, y1) = (4, 7) in Eq (2)

y - 7  =  -1/2 (x - 4) 

2(y - 7)  =  -1 (x - 4) 

2y - 14  =  -x + 4 

x + 2y  =  4 + 14

x + 2y = 18

Answer :

The equation of line BC is x + 2y = 18.