Question

Helphelphelphelphelphelphelp!!!!!!!!!!!! Please!!!!!!!!!!!!!Somebody!!!!!!! Dx<

In the diagram Q is the midpoint of segment PR. Show that PQ and QR are each equal to 1/2PR.
Given-> Q is the midpoint of segment PR
Prove->PQ=1/2PR and QR=1/2PR

Answer 1

can you scan the pic?

Answer 2

ok im going to divide it up first lets determine midpoint Q
which is
Q's x co-ordinate= (Px+Rx)/2
Q's y co-ordinate= (Py+Ry)/2

Answer 3

now lets determine what the length PR is equivalent to:
we use the distance formula
\[D=\sqrt{(x2-x1)^2+ (y2-y1)^2}\]

Answer 4

\[PR=\sqrt{(Px2-Rx1)^2+(Py2-Ry1)^2}\]

Answer 5

now we have to show distance between QP and QR is 1/2 of what we got for PR

Answer 6

\[PQ=\sqrt{((2Px/2)-(Px+Rx)/2)^2+((2Py/2)-(Py+Ry)/2)^2}\]

Answer 7

that was simplified form tell me if u didnt get it

Answer 8

\[PQ=\sqrt{((Px1-Rx1)/2)^2+((Py1-Ry1)/2)^2}\]

Answer 9

u \[PQ=\sqrt{(Px1-Rx1)^2/4)+(Py1-Ry1)^2/4}\]

Answer 10

\[PQ=1/2\sqrt{(Px1-Rx1)^2)+(Py1-Ry1)^2}\]

Answer 11

the quarter gets square rooted and u end up with a half infront of the equation

Answer 12

U ARE WELCOME RAINBOW MONKEY!!!!

Answer 13

I can't see the diagram..

Answer 14

there's no need for diagram

Answer 15

its for any arbitrary line

Answer 16

Oh, sorry. I misread.

Answer 17

it is right i think

Answer 18

is it hard to follow?

Answer 19

@polpak

Answer 20

kushawa is there anyway u can take medal back other ppl might not attempt if it says good answer

Answer 21

Sorry, yeah. just trying to confirm your reasoning.

Answer 22

didn't understand what u mean hahd

Answer 23

if its not right no one else will attempt it

Answer 24

the medal should be given if only sure

Answer 25

ok , but i am sure sorry , carry on

Answer 26

no worries i know u mean well

Answer 27

ok , polpak whenever u get free from this problem come here whever u get time for me
http://openstudy.com/groups/mathematics#/groups/mathematics/updates/4e532bac0b8b958804b81d0d

Answer 28

The midpoint formula is:
\[Q = \left(\frac{P_x + R_x}{2}, \frac{P_y + R_y}{2}\right)\]

Therefore the Distance from P to Q is:

\[D_{PQ} = \sqrt{\left( \frac{P_x + R_x}{2} - P_x\right)^2 + \left( \frac{P_y + R_y}{2} - P_y\right)^2 }\]\[=\sqrt{\left( \frac{R_x}{2} - \frac{P_x}{2}\right)^2 + \left( \frac{R_y}{2} - \frac{P_y}{2}\right)^2 }\]\[=\sqrt{\frac{1}{4}[ \left(R_x - P_x\right)^2 + \left(R_y - P_y\right)^2]}\]\[= \frac{1}{2}\sqrt{ \left(R_x - P_x\right)^2 + \left(R_y - P_y\right)^2} =\frac{1}{2} D_{PR}\]

Then do the same for QR

Answer 29

so its right?

Answer 30

Yes

Answer 31

YES!!!!!!!

Answer 32

thnkx bro

Answer 33

i said u u r right

Answer 34

Thank you Fairy Tail!!!!! xD