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The line 3x-4y=5 intersects the $x$-axis and $y$-axis at points $A$ and $B,$ respectively. Find the distance $AB.$

 
 Jan 1, 2025
 #1
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3x - 4y  = 5

 

x axis intersection , let y = 0

3x = 5

x = 5/3

 

y axis intersection, let x =0

-4y = 5

y = -5/4

 

AB  = sqrt  [ (5/3)^2  + (-5/4)^2 ] =   sqrt [ 25/9 + 25/ 16 ]  = [ sqrt [ (9 + 16)(25) / (16 * 9) ] = 

 

sqrt [ 25^2 / 144]  =   25 / 12

 

cool cool cool

 Jan 1, 2025

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