Help Please!!! How do you figure out if something is an ISOSCELES TRAPEZOID

Pre-calc/Geometry Problem Help? please :) Isosceles Trapezoid...?
Do the vertices/points
( - 4 , - 5 ) , ( - 3 , 0 ) , ( 0 , 2 ) and ( 5 , 1 )
make an isosceles trapezoid?


Okay well I've tried asking similar question here recently and no one answered, so I'm not going to ask for mathematical proof/evidence,

but I do have one question!!!



********** Please, can someone tell me how can you figure it out if specific points create an Isosceles Trapezoid??? **********

like can someone tell me if i have to solve with angle measurements in the math equation or something?

Please?

I really need assistance in this problem, I have no idea what to do :(

thank you so much...

First, please mark the points given on a scaled paper and name the points :

A( - 4 , - 5 ) ,
B( - 3 , 0 ) ,
C( 0 , 2 ) and
D( 5 , 1 )

Draw lines from A to B to C to D in that order.

OK.

Now, to have a isosceles trapezoid we must prove that BC // AD ( the slope of this lines are equal)
and AB = CD

m = (y2 - y1) / (x2 - x1)
m(BC) = (2-0)/(0+3) = 2/3
M(AD) = (1+5)/(5+4) = 6/9 = 2/3

therefore BC // AD

AB = CD?

draw a perpendicular line from A on OX axis (name the intersection Q) and a line from D on OY axis (name that ...Q)

you will have right triangles where:

AB = sqrt(QB^2 + AQ^2)
QB = |-3 +4 | = 1
AQ = | 0 - (-5)|= 5

====> AB = sqrt(26)

same method for CDP triangle:
CD = sqrt (PC^2 + DP^2) = sqrt (26)

CD = AB and BC // AD ===> isosceles trapezoid

You have to graph the points first in order to see if it is a trapezoid. A trapezoid needs 1 pair of parallel sides (top and bottom). The sides of the trapezoid (right and left) have to be the same length and opposite slopes. You also have to make sure the height is the same, just count the boxes inside the trapezoid from up to down. Once you have that solved, you know its a trapezoid.

Hope this helped.