Question

Find the slope of each side of the triangle: A(-3,5) B(2,6) C(-5,-2)​

Answer 1

`{\sf AB}`:
`(1/5)`.

`{\sf BC}`:
`(8/7)`.

`{\sf AC}`:
`(7/2)`.

Explanation:

Let
`(x_(0),\, y_(0))` and
`(x_(1),\, y_(1))` denote two points in the plane. As long as
`x_(0) \\e y_(0)` (that is, these two points are not on the same vertical line,) the slope of the line between these two points would be:

`\displaystyle (y_(1) - y_(0))/(x_(1) - x_(0))`.

For example, for side
`{\sf AB}`,
`x_(0) = (-3)` and
`y_(0) = 5` (for point
`{\sf A}` at
`(-3,\, 5)`) while
`x_(1) = 2` and
`y_(1) = 6` (for point
`{\sf B}` at
`(2,\, 6)`.)

Since
`x_(0) \\e x_(1)`, the slope of the line between
`{\sf A}` and
`{\sf B}` would be:

`\begin{aligned}m({\sf AB}) &=(6 - 5)/(2 - (-3)) \\ &= (6 - 5)/(2 + 3) \\ &= (1)/(5)\end{aligned}`,

Likewise:

`\begin{aligned}m({\sf BC}) &=((-2) - 6)/((-5) - 2) \\ &= ((-8))/((-7)) \\ &= (8)/(7)\end{aligned}`.

`\begin{aligned}m({\sf AC}) &=((-2) - 5)/((-5) - (-3)) \\ &= ((-7))/((-2)) \\ &= (7)/(2)\end{aligned}`.