Question

Show that PQRS is a rectangle.
(P: (1,4); Q: (2,6); R: (8,3); S: (7,1)

Answer 1

I did this for you , it was #5 of
http://www.jiskha.com/display.cgi?id=1386029033

Ok, once more, very simple:

slope PQ = (6-4/(2-1) = 2
slope QR = (6-3)/(2-8) = -3/5

So there is no right angle at Q

but a rectangle must have 4 right-angles
I have shown that one of them is not, so there is no point to continue

It is NOT a rectangle

Answer 2

P: (1,4); Q: (2,6); R: (8,3); S: (7,1)

PQ = (6-4)/(2-1) = 2/1 = 2

QR = (3-6)/(8-2) = -3/6 = -1/2

RS = (1-3)/(7-8) = 2

PS = (1-4)/(7-1) = -3/6 = -1/2

The slopes of all of consecutive sides are negative reciprocals. Therefore, quadrilateral PQRS with 4 angles is a rectangle.

Answer 3

sorry about my arithmetic error

when I copied your diagram to paper, I had point
Q as (3,6) instead of (2,6)