Help with slopes and cooridinates (trapezoid midsegment)

[platinum292]

Here is one of the questions

Find the slope of the midsegment of trapezoid ABCD given A(-2,-4), B(4,2), C(8,4), and D (-4, -8)

Can someone show me how to solve this?

 

[Loren]

Re: Help with slopes and cooridinates

I suggest you get out a sheet of graph paper and draw the trapezoid described. The midsegment of a trapezoid, I believe, has the same slope as the two parallel sides. Therefore, you can determine the end points of one of the parallel sides and use those points to calculate the slope.

 

[Mrspi]

Here is one of the questions

Find the slope of the midsegment of trapezoid ABCD given A(-2,-4), B(4,2), C(8,4), and D (-4, -8)

Can someone show me how to solve this?

Loren has given you an excellent approach. Did you GRAPH these points and draw the trapezoid? I'd SURELY do that as my first step.

A midsegment of a trapezoid joins the midpoints of the two non-parallel sides.

Once you've plotted the points, and drawn the trapezoid, you should be able to see which sides are the non-parallel ones. Now, you know the endpoints of these sides (they are some of your GIVEN points).

Remember how to find the midpoint of a segment? If the endpoints of the segment are (x[sub:fd47449i]1[/sub:fd47449i], y[sub:fd47449i]1[/sub:fd47449i]) and (x[sub:fd47449i]2[/sub:fd47449i], y[sub:fd47449i]2[/sub:fd47449i]), then the midpoint of the segment is ( (x[sub:fd47449i]2[/sub:fd47449i] + x[sub:fd47449i]1[/sub:fd47449i])/2 , (y[sub:fd47449i]2[/sub:fd47449i] +y[sub:fd47449i]1[/sub:fd47449i])/2 )

Find the two midpoints...then use the definition of slope to find the slope of the midsegment (and Loren is correct...the midsegment is parallel to each of the bases of the trapezoid)

 

[masters]

Just find the slope of one of the bases. That'll be the same as the midsegment and a lot quicker.

 

[stapel]

Just find the slope of one of the bases....

And how is the student to determine which point-pairs mark the endpoints of the bases, without graphing and / or finding all four slopes? (And even the slope "method" assumes that the points have been labelled "in order", so that, for instance, AC is not a side. How is this to be determined without a graph?)

Note: After having done the graph and having confirmed which sides are which, your "method" is exactly what the first tutor said.

Eliz.