Question

The endpoints of a side of rectangle ANCD in the coordinate plane are at A(3,5) and B(5,1). Find the equation of the kind that contains the given segment. The line segment is AB.

The equation is y=
PLEASE HELP VERY URGENT :(

Answer 1

The equation of the line segment AB is:

`y = -2x+11`

The graph of the line segment AB is also attached.

Explanation:

Given the points

• A(3,5)

• B(5,1)

Determining the slope between A(3,5) and B(5,1)

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

`\left(x_1,\:y_1\right)=\left(3,\:5\right),\:\left(x_2,\:y_2\right)=\left(5,\:1\right)`

`m=(1-5)/(5-3)`

`m=-2`

Using the point-slope form of the line equation

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

where m is the slope of the line and (x₁, y₁) is the point

substituting the values m = -2 and the point (3, 5) in the equation

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

`y - 5 = -2(x-3)`

`y-5 = -2x+6`

`y = -2x+6+5`

`y = -2x+11`

Therefore, the equation of the line segment AB is:

`y = -2x+11`

The graph of the line segment AB is also attached.