A line is drawn through the points A(0,16) and B(8,0). Point P is chosen in the first quadrant on the line through A and B. Points C and D are chosen on the x and y-axis respectively, so that PDOC is a rectangle, where O is the origin?

Number of possible ordered pairs of all positions of the point P on AB so that the area of the rectangle PDOC is 30 sq.units is?

1 Answer
CW
Oct 16, 2017

number of possible ordered pairs #=2#

Explanation:

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Given that a line passes through #A(0,16) and B(8,0)#,
equation of the line is #x/8+y/16=1# ------ EQ (1)
Given that area of rectangle #PDOC = 30 " unit" ^2#,
#=> x*y=30#
#=> y=30/x#,
substituting #y=30/x# in EQ (1),
#=> x/8+30/(16x)=1#

#=> x^2-8x+15=0#
#=> (x-3)(x-5)=0#
#=> x=3 or 5#
#=> y=10 or 6#
#=># ordered pairs #(x,y)=(3,10), (5,6)#

Hence, number of ordered pairs #=2#

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