Question

The endpoints of a side of rectangle ABCD in the coordinate plane are at A(3, 5) and B(5, 1). Find the equation of the line that contains the given segment. The line segment is CD and point C is at (7, 2

Answer 1

2x + y = 16

Explanation:

In rectangle side AB and side CD are parallel, so the slope of both the lines will be same it means that they are parallel to each other.

slope of line AB:

`\textrm{m}=\frac{\textrm{y}_(A)-\textrm{y}_(B)}{\textrm{x}_(A)-\textrm{x}_(B)}\\\textrm{m}=(5-1)/(3-5)=(4)/(-2)=-2\\\therefore \textrm{m}=-2`

slope of line CD = slope of line AB = -2

∴ equation of line CD:

`\textrm{y}-\textrm{y}_(C)=\textrm{m}(\textrm{x}-\textrm{x}_(C))\\ \textrm{y}-2=-2(\textrm{x}-7)\\2\textrm{x}+\textrm{y}=16`