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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          
(d) none of these



Answer -

Equationis 4x + 3y = 12
If it cuts the x-axis, then y = 0
∴ 4x x 3 x 0 = 12
⇒ 4x = 12 ⇒ x = 12 =3
OA = 3 units
∴ Thepoint of intersection of x-axis is (3, 0)
Again if it cuts the y-axis, then x = 0 , Y= 0
∴ 4x x 3 x 0 = 12
⇒4x = 12 ⇒ x=  12 =4
⇒ OB= 4 units
∴ Thepoint of intersection is (0, 4)
∴ Inright ΔAOB,
AB2 = AO2 +OB2
= (3)2 + (4)2
= 9 + 16 = 25
= (5)2
∴ AB = 5units                                        (c)

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