Question

Geometry help please!!! :) A trapezoid is drawn on a grid with vertices at P (-5,7), Q (-2,7), R (2,3), and S (-8,3). Trapezoid UVWX will be drawn similar to trapezoid PQRS with side UV corresponding with side PQ. The point (2,2) will be the location of vertex U and point (8,-2) will be the location of point V. What will be the coordinates of vertex X? Show all your work or explain your reasoning.

Answer 1

I assume you have plotted the points on the graph already @Christawna~Marie

Answer 2

Yeah, I tried that...but, I'm still confused.. :/

Answer 3

find the distance between points P and U
Also find the slopes between those points
Move point S to that distance with the same slope

Answer 4

It's not that simple @niravshah08

Answer 5

The second trapezoid is larger and it has rotated clockwise

Answer 6

Besides, its the coordinates of point X we're looking for, not point S

Answer 7

ohh sorry, i din't go through the points
In that case we can divide the distances PQ/Dist UV to get a ratio, since both are similar
And then use the ratio to figure out remaining distances
then find their intersection points
which will give us the co-ordinates
idk if this will wrk....just guessing

Answer 8

I have the distance and slope for point P and U....however, I'm still not sure what that have to do with the answer that I need...in other words I'm still confused and dont know what to do to get the answer @ niravshah08.

Answer 9

Hold on lemme graph

Answer 10

intersection points?....why do I need intersection points ....I need to understand because I dont know what I'm doing....

Answer 11

I dont know if this matters or not but I started trying to figure out the problem and this is what I started with....
PQ= 3:1
QR= 4:4
RS= 10:1
SP= 3:4
UV:6:1

but then I got stuck...I dont know if I even started the right way in solving this...

Answer 12

I'm going to try plotting everything on the graph again..maybe I made a mistake or something...

Answer 13

Ok i figured it out
Firstly, you need to draw all the six given points on a grid paper in a X,Y axis and follow all explanations in the drawing.

From the names of the vertices of the trapezoids: UVWX and PQRS we see that UV corresponds with PQ, and UX with PS.

From the drawing we see that length of segment PQ is 3 units (subtract the x values) and the length of the segment UV is 9 units, so we already know that all sides of the the second trapezoid are 3 times as long as the corresponding sides in the original trapezoid.

Now we need to find point X.

In the original trapezoid PQRS, draw a line through P, perpendicular to SR to arrive at a new point P' (-5, 3)

This shows you that to arrive at point S starting from point P you need to go left 3 units and go down 4 units.
As we know that in the second trapezoid all sixes are 3 times as large, so to arrive at point X from point U, for the x coordinate you need to go left 3 times 3 = 9 units and for the y coordinate you go 3 times 4 = 12 units down.

U is at (-2,-1). So to arrive at point X you calculate the coordinates as follows: (-2-9, -1-12) ie. (-11,-13)

Answer 14

got it from yahoo answers

Answer 15

Wow, you're a cheater @niravshah08 :P

Answer 16

lol i gave credits to yahoo answer, and plus i dont hve a pen and paper handy to graph it all :P

Answer 17

Okay thanks @niravshah08 :)

Answer 18

thanks @ Hero also for your help. :)

Answer 19

@Hero actually worked the problem, keep it up man