Question

The endpoints of a side of rectangle ABCD in the coordinate plane are at A(1, 6) and

B(6, 1). Find the equation of the line that contains the given segment.

The line segment is AB.

The equation is y =

Answer 1

The equation is:

`y = -x + 7`

Explanation:

Given the endpoints of a side of a rectangle

• A(1, 6)

• B(6, 1)

Finding the slope

`\mathrm{Slope}=(y_2-y_1)/(x_2-x_1)`

`\left(x_1,\:y_1\right)=\left(1,\:6\right),\:\left(x_2,\:y_2\right)=\left(6,\:1\right)`

`m=(1-6)/(6-1)`

`m=-1`

Using the point-slope form of a line equation

`y-y_1=m\left(x-x_1\right)`

substituting the values m = -1 and the point (1, 6)

`y - 6 = -1 (x - 1)`

`y - 6 = -x + 1`

`y = -x + 1 + 6`

`y = -x + 7`

Thus, the equation is:

`y = -x + 7`