Question

The coordinates of the vertices of quadrilateral JKLM are J(-3,2), K(4,-1), L(2,-5) and M(-5,-2). Find the slope of each side of the quadrilateral and determine if the quadrilateral is a parallelogram?

Answer 1

JKLM is a parallelogram

Explanation:

The slope `m` of a line through two points `(x_1, y_1)` and `(x_2, y_2)` is given by the formula:

`m = (Delta y)/(Delta x) = (y_2 - y_1)/(x_2 - x_1)`

So the slopes of the sides of our quadrilateral are:

`m_(JK) = ((-1)-2)/(4-(-3)) = -3/7`

`m_(KL) = ((-5)-(-1))/(2-4) = 2`

`m_(LM) = ((-2)-(-5))/(-5-2) = -3/7`

`m_(MJ) = (2-(-2))/((-3)-(-5)) = 2`

So `JK` is parallel to `LM` and `KL` is parallel to `MJ`

So `JKLM` is a parallelogram.