PQRS is a rectangle with vertices P(-3,2) and Q(-1,-5) and PQ=2(QR). Find all possible coordinates of R and S

Question

HELP! DUE TODAY!

Answer 1

Dd you draw and label the points?

As Adam P. state the orthagonal is 2/7. To be twice as long Q and R must be 4/14.

So R is at either at (-1 + 14, -5 + 4) or (-1 - 14, -5 - 4)

Q is at either... well you calculate.

Answer 2

Length of PQ = √53

The Equation of line passing through Q orthogonal to PQ, namely line QR ,is y =(2/7)x -33/7

Now we are in search of two points on QR whose distance from Q is ( √53) /2.

Notice that every point on QR has coordinates [ x, (2/7)x -33/7 ]

Then ( x +1 )² + { (2/7)x -33/7 +5 }² = 53/4

( x +1 )² + ( 4/49) (x+1)²= 53/4

( x +1 )² = 1 Hence x =0 or x = -2

That is R_x = 1 or R_x = -2 and since the R belongs to line QR with equation y =(2/7)x -33/7 you can calculate easily the y-coordinates of the potential R points being either R( 0, -33/7 ) or R ( -2, -37/7)

For the rest of the problem my friend the ball now is in your court