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### Ben Evans says

Point P is: (2+-1)/2, (9+3)/2=1/2, 6

Point Q is: (5+-1)/2, (-2+3)/2=2, 1/2

Point R is: (5+5)/2, (-2+4)/2=5, 1

Point S is: (2+5)/2, (9+4)/2=7/2, 13/2

AC is a line with a slope ( -2-9)/(5-2)=-11/3

Y=mx +b form=======> 9=-11/3(2)+b. b=49/3 Y=-11/3X+49/3

BD is a line with a slope (4-3)/(5-{-1})=1/6

Y=mx+b form=========>4=1/6(5) +b b=19/6 Y=1/6X+19/6

Set both to equal -11/3X+49/3=1/6X+19/6

Common dem============>-22/6X+98/6=1/6X+19/6

so 23/6X=79/6 X=79/23 so........

Y=1/6(79/23)+19/6=79/138+437/138= 516/138=86/23

So the intersection point 79/23, 86/23

### mdkshareef says

mid point of AB is P = (1/2,6)

mid point of BC is Q = (2,1/2)

mid point of CD is R = (5,1)

mid point of AD is S = (7/2,13/2)