Question

The endpoints of a side of rectangle ABCD in the coordinate plane are at A (2, 11) and
B (7, 1). Find the equation of the line that contains the given segment.

The line segment is AD.

What is the Equation?

Answer 1

ANSWER

$2y-x-20=0$

or

$y=\frac{1}{2}x+10$

EXPLANATION

Let the rectangle be oriented as shown in the diagram.

The line segment AD passes through $A(2,11)$.

All we need now is the slope of AD then we can find its equation.

Since AD is perpendicular t AB, we determine the slope of AB and then use it to find the slope of AD.

$Slope_{AB}=\frac{1-11}{7-2}$

$Slope_{AB}=\frac{-10}{5}=-2$

The slope of AD is the negative reciprocal of the slope of AB because they are perpendicular.

$Slope_{AD}=\frac{-1}{-2}=\frac{1}{2}$

The equation of AD is given by;

$y-y_1=m(x-x_1)$

$y-11=\fra[1}{2}(x-2)$

Multiplying through by 2 gives,

$2y-22=(x-2)$

$2y-x-22+2=0$

$2y-x-20=0$

or

$y=\frac{1}{2}x+10$