Question

PLEASE HELP MEEE :( consider the points P (-3, 0), Q (a, b) R (3, -3) and S (b+2,a+5). find the coordinates of Q and S if figure PQRS forms a parallelogram.

okay so what i did is equate the slope and distances of lines PQ and RS... but i'm still not getting a final answer :(

Answer 1

slope pq= slope rs--> b/(a+3)=(a+8)/(b-1)
distance pq = distance rs --> (a+3)^2+b^2=(b-1)^2+(a+8)^2 so b=5a+28

tried to do systems but then there's no answer?!?!?! based on http://www.wolframalpha.com/input/?i=%28a%2B3%29%5E2%2Bb%5E2%3D%28b-1%29%5E2%2B%28a%2B8%29%5E2%3B+b%2F%28a%2B3%29%3D%28a%2B8%29%2F%28b-1%29 huhuhu someone help please :((

Answer 2

did you try solving it with vectors?

Answer 3

im thinking of midpoints :)

Answer 4

(P+R)/2 = (Q+S)/2

P+R = Q+S

Answer 5

but that just gets me parallel lines that have no solution :/

a+b = -2
a+b = -8

Answer 6

is there a figure to pull information off of?

Answer 7

we need to develop a notion of the rule that defines Q and S to narrow down the options eh

Answer 8

what did you mean by your last message, amistre64? btw, is there anything wrong with my solution?

Answer 9

a parallelagram is defined as opposite sides are parallel; i was just looking for "orbits" that would define the possibilities of 2 other points.

Answer 10

ghass1978, nope i don't remember how to use vectors... it's not part of our exam. sorry

Answer 11

your initial ideas look good in that they are defining valid properties

Answer 12

is there a diagram that goes with this? or is it just a wordy problem?

Answer 13

just that, exactly that :( waaaaahhh :(

Answer 14

but it says PQRS which means the sequence of the coordinates would be that way. as in Q "between" P and R... if that's what you're wondering

Answer 15

without using the relationship between Q and S, we can get any number of values for Q and S