Q23 of 50 Page 4

If the graph of 4x + 3y = 12, cuts the coordinate axes at A and B. And if O is the origin, find the hypotenuse of ΔAOB.

Given Equation: 4x + 3y = 12


At A, it cuts the x-axis, therefore, y = 0,


4x + 0 = 12


x = 3


So, first point is A(3, 0)


Now, at B it cuts the y-axis, therefore x = 0,


0 + 3y = 12


y = 4


So, the second point is B(0, 4).



Now, in ΔAOB,


(AB)2 = (OA)2 + (OB)2


(AB)2 = 32 + 42


(AB)2 = 9 + 16 = 25


AB = 5 units.


Hence, the length of hypotenuse of ΔAOB is 5 units.


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