Need help understanding how to do this.

Question

Given quadrilateral LMNO with the following calculations of slopes and lengths, what is the best descriptive name for quadrilateral LMNO (Trapezoid, Isosceles Trapezoid, Parallelogram, Rhombus,

Rectangle, or Square).

Slopes of Sides Slopes of Diagonals

slope LM: -3 slope LN: 13/9

slope MN: 1/3 slope MO: -1/3

slope NO: -3

slope OL: 1/3

Answer 1

Hello Shelly,

I will get you started on this one. It will also help you with your other question.

If slopes are equal then lines are parallel. If slopes are negative inverses (product is -1), then the lines are perpendicular (form right angles).

In your problem, -3 and 1/3 are negative inverses, so you will have some right angles. Draw a picture of LMNO and mark the right angles and parallel sides. Then you should be able to tell what shape it is. The diagonals are not perpendicular (13/9 and -1/3) so that eliminates squares and rhombuses which must have perpendicular diagonals.

Your other question has an extra step at the beginning of finding the slopes yourself. You can take any two points and use the formula (y₂ - y₁)/(x₂ - x₁) to find the slope. Make a list of the results of the slope for each side and diagonal like what was given to you in this problem.

Now see if you can finish up those two problems!