Question

Rectangle ABCD has two vertices at coordinates A(-1,-3) and B(6,5). The slope of BC is...

Answer 1

slope of BC = -
`(7)/(8)`

Explanation:

Given vertices A and B then the side BC is perpendicular to AB

calculate the slope m of AB using the slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

let (x₁, y₁ ) = A (- 1, - 3 ) and (x₂, y₂ ) = B (6, 5 )

substitute these values into the formula for m

`m_(AB)` =
`(5-(-3))/(6-(-1))` =
`(5+3)/(6+1)` =
`(8)/(7)`

given a line with slope m then the slope of a line perpendicular to it is

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/((8)/(7) )` = -
`(7)/(8)`

the slope of side BC = -
`(7)/(8)`