Question

A parallelogram has one side at (-4, 1) and (-7, 2) and the other side is at (-3, 4) and (-6, 5). What are the lengths of the sides and the slopes of the sides?

Answer 1

`AB = CD = sqrt(10)` units,

Slope of `AB` = Slope of `CD` = `-1/3`

Explanation:

For our work to be easier, We will assume the points as `A(-4, 1), B(-7, 2), C(-3, 4) and D(-6, 5)`.

Now, As per the Question,

We need to find the lengths of the sides.

Just use the Distance Formula.

Distance Between the Two Points `(x_1, y_1), (x_2, y_2)` = `sqrt((x_1 - x_2)^2 + (y_1 - y_2)^2)`

Now,

`AB = sqrt((-4 + 7)^2 + (1 - 2)^2) = sqrt(9 + 1) = sqrt(10)` units.

Similarly, `CD = sqrt((-3 + 6)^2 + (4 - 5)^2) = sqrt(9 + 1) = sqrt(10)` units.

[Interesting Thing To Observe: Those are opposite sides of the parallelogram, so they are same....]

Now, The slopes.

Use the Point-Slope Form of the Linear Equation.

Point Slope Form :- `m = (y_2 - y_1)/(x_2 - x_1)` if `(x_1, y_1)` and `(x_2, y_2)` are two points on the line.

So, Slope of `AB = (2 - 1)/(-7 + 4) = 1/-3 = -1/3`.

And Slope of `CD = (5 - 4)/(-6 + 3) = -1/3`.

[Again, an Interesting Thing :- The opposite sides of a parallelogram are parallel, and the slopes of parallel lines are equal].

Hope this helps.