Question

In quadrilateral PQRS, the coordinates are P(0, 0), Q(a + c, 0), R(2a + c, b), and S(a, b). How can you use coordinate geometry to show that the diagonals are perpendicular?

A. Apply the Distance Formula to show that opposite sides line PQ and line RS are congruent.
B. Find the slopes of line PQ and line RS , and show that their product is 1.
C. Apply the Distance Formula to show that opposite sides line PS and and line QR are congruent.
D. Find the slopes of line PR and line QS , and show that their product is -1.

Answer 1

so, do you know distance formula and slope formula ?

Answer 2

Distance between points (x1,y1) and (x2,y2) is
\(\huge d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\)

The slope of the line through points (x1,y1) and (x2,y2) is given by :
\(\huge m=\frac{y_1-y_2}{x_1-x_2}\)

Answer 3

I dont understand this ?

Answer 4

"Apply the Distance Formula to show that opposite sides line PQ and line RS are congruent."

so we need to find PQ and RS
and you know co-ordinates of all 4.
so try to apply the distance formula and find PQ first ?

Answer 5

the same way you did for your previous prolem

Answer 6

PQ = sqrt (0-a+c)^2+(0-0)^2 ?? like this ?

Answer 7

[0 - (a+c) ]^2
be careful with brackets

Answer 8

\(PQ = \sqrt{[0-(a+c)]^2+0} = a+c\)

Answer 9

ok but what's the answer am gonna get for this equation ?

Answer 10

so thats PQ
try to find RS now ?

Answer 11

ok

Answer 12

then in same way find
PS and QR too for part C

Answer 13

RS = sqrt [ (2a+c) - a ] ^2 + [ b-b ] ^2

Answer 14

good, simplify that...

Answer 15

and how do I do that ?

Answer 16

(2a+c) - a = 2a-a +c = ... ?

Answer 17

i got 0 ? they're kinda the same

Answer 18

didn't you get a+c for both PQ and RS ?

which is what we wanted to prove , that PQ= RS

Answer 19

now find PS And QR using same distance formula, and check whether they come out to be same

Answer 20

yea
sorry am not good at this thing so I don't know how to the things you're telling me

Answer 21

actually, its the same way you found PQ
you did it on your own.
whats the problem in finding PS and QR in same way ?

Answer 22

is it C ?

Answer 23

or A

Answer 24

we're done with A, now we're trying to solve part C

Answer 25

so A is not the answer
so we're gonna repeat everything we did before but with PS and QR

Answer 26

ok, lets use slope formula.

find slope between PQ and RS first.

Answer 27

P(0, 0), Q(a + c, 0)

so,
\(
\large m= \dfrac{0-0}{a+c-0} =... ? \)

Answer 28

\[\frac{ 0 }{ a+c }\]

Answer 29

which is 0

so the product won't be -1! right ??

for lines to be perpendicular, the product of slopes should be -1
and since its not option B, which option remains ?

Answer 30

if the slope should be -1 then its D

Answer 31

the 'product' of slopes should be -1
and yes, its D :)

Answer 32

ok thanks a lot

Answer 33

welcome :)

Answer 34

can you help me with this http://openstudy.com/study#/updates/533bb2fee4b06e93c844f393