Question

If the graph of the linear equation 24x+7y=168 cuts the x-axis and y-axis at A and B respectively,then length of AB is equal to
1)25 units
2) 7 units
3) 24 units
4) 31 units​

Answer 1

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Answer 2

Answer: 1)The distance is 25 units

Step-by-step explanation:

The linear equation in two variable is 24x+ 7y =168

when the line cuts x axis ; y= 0

therefore

$24x+ 7(0) = 168 \Rightarrow x= \dfrac{168}{4} =7$

So the coordinate is  (7,0)

when the line cuts  y axis ; x= 0

therefore

$24(0) + 7y= 168 \Rightarrow y= 24$

So the coordinate is (0,24)

By distance formula we have  

$\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} = \sqrt{(0-7)^2+ (24-0)^2}\\\\ =\sqrt{49+576}= \sqrt{625} =25$

Hence the distance is 25 units