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Question

The vertices of a quadrilateral, taken in order, are the points (0,0), (4,0), (6,7), and (0,3); find the coordinates of the point of intersection of the two lines joining the middle points of opposite sides.

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Solution


A(0,0),B(4,0),C(6,7),D(0,3)

Mid point of AB

P(0+42,0+02)P(2,0)

Mid point of BC

Q(4+62,0+72)Q(5,72)

Mid point of CD

R(6+02,7+32)R(3,5)

Mid point of DA

S(0+02,3+02)S(0,32)

Equation of line joining PR

y0=5032(x2)y0=5x105xy=10........(i)

Equation of QS

y72=327205(x5)y72=25(x5)5(2y7)=4(x5)10y35=4x2010y4x=15......(ii)

Solving (i) and (ii)

x=52,y=52

So the point of intersection is (52,52)


694621_640686_ans_24786e0e7da04233842f30356b27e4d1.png

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