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Question -

If the graph of the equation 4x + 3y = 12 cuts the co-ordinate axes at A and B, then hypotenuse of right triangle AOB is of length
(a) 4 units
(b) 3 units
(c) 5 units┬а ┬а ┬а ┬а ┬а┬а
(d) none of these



Answer -

Equationis 4x + 3y = 12
If it cuts the x-axis, then y = 0
тИ┤┬а4x x 3 x 0 = 12
тЗТ┬а4x = 12 тЗТ┬аx =┬а12┬а=3
OA = 3 units
тИ┤ Thepoint of intersection of x-axis is (3, 0)
Again if it cuts the y-axis, then x = 0 , Y= 0
тИ┤┬а4x x 3 x 0 = 12
тЗТ4x┬а= 12┬атЗТ x=┬а┬а12┬а=4
тЗТ┬аOB= 4 units
тИ┤ Thepoint of intersection is (0, 4)
тИ┤ Inright ╬ФAOB,
AB2┬а= AO2┬а+OB2
= (3)2┬а+ (4)2
= 9 + 16 = 25
= (5)2
тИ┤ AB = 5units┬а┬а┬а┬а┬а┬а┬а┬а┬а┬а┬а┬а┬а┬а┬а┬а┬а┬а┬а┬а┬а┬а┬а┬а┬а┬а┬а┬а┬а┬а┬а┬а┬а┬а┬а┬а┬а┬а┬а┬а(c)

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