Question

The endpoints of a side of rectangle ABCD in the coordinate plane are at A (1, 11) and B (3, 1). Find the equation of the line that contains the given segment. The line segment is AD.

Answer 1

Coordinates of vertices of rectangle A B CD are A(1,11), B(3,1).

Equation of line AB is

`(y-1)/(x-3)=(1-11)/(3-1)`

`(y-1)/(x-3)=-10/2`

⇒y-1=-5(x-3)

⇒y-1= -5 x+15

⇒y+ 5 x=1+15

⇒y+5 x=16→[ Equation of line that contains line segment AB]

Equation of line perpendicular to AB is

x- 5 y +k=0

Since it passes through A(1,11).

1-5×11+k=0

1-55+k=0

k-54=0

k=54

So equation of AB is

x-5 y+ 54=0

So equation of line, containing line segment AD is

→x-5 y+54=0