SOLUTION: What are the coordinates of points Q and R where Q is on {{{ y=(1/2)x-2 }}} and R is on {{{ y= -x+5 }}} and a line is drawn from P to intersect with the lines so that P is the midp

We let the x-component of Q be a, Then since Q is on the line
, the y-component of Q is found by substituting
a for x in  and get . So
Q is the point Q(a,),

We let the x-component of R be b, Then since R is on the line
, the y-component of R is found by substituting
b for x in  and get . So
R is the point R(b,-b+5)



We are told that P(1,1) is the midpoint of QR.  We use the
midpoint formula:

Midpoint = 

Midpoint = 

So we equate those coordinates to the coordinates of P(1,1).

Equating the x-coordinates of P




Equating the y-coordinates of P





Multiply through by 2:



So we solve the system by substitution or elimination:


Solve the first for a=2-b
Substitute in the second equation:
(2-b)-2b=-2
  2-b-2b=-2
    2-3b=-2
     -3b=-4
       b=

a=2-b
a=2-
a=
a=

So the point  becomes:









So the point R(b,-b+5) becomes:







Edwin