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A(2,9) B(-1,3) C(5,-2),D(5,4) are the vertices of a quadrilateral and P,Q,R,S are the midpoint...

of the side AB,BC,CD and AD respectively.

Find the coordinates of P,Q,R,S

Also,find the coordinates of the point of intersection of AC and BD.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)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

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