Question 77

The length of the portion of the straight line 3x + 4y = 12 intercepted between the axes is

Solution

Equation : $$3x + 4y = 12$$

To find $$x$$-intercept, put $$y$$=0

=> $$3x + 0 = 12$$

=> $$x$$ = 4

Similarly to find $$y$$-intercept, we need to put $$x$$ = 0

=> $$0 + 4y = 12$$

=> $$y$$ = 3

Thus, the line passes through (4,0) in x-axis and (0,3) in y-axis

Using, $$d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$$

=> $$x_1 = 0 , x_2 = 4 , y_1 = 0 , y_2 = 3$$

=> $$d = \sqrt{4^2 + 3^2}$$

=> $$d = \sqrt{25} = 5$$

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