the equation of line a is y = 4 / 3 * x - 100. what is the smallest possible distance in the xy - plane from the point with coordinates ( 0, 0 ) to any point on line a?
Pick.
A) 48
B) 50
C) 60
D) 75
E) 100
<gadget id="calculator">100 * 3</gadget>
<output>300</output>

<gadget id="calculator">4 ** 2</gadget>
<output>16</output>

<gadget id="calculator">3 ** 2</gadget>
<output>9</output>

<gadget id="calculator">16 + 9</gadget>
<output>25</output>

<gadget id="calculator">25 ** (1/2)</gadget>
<output>5</output>

<gadget id="calculator">300 / 5</gadget>
<output>60</output>

<result>C</result>
the equation of line a is y = 4 / 3 * x - 100. what is the smallest possible distance in the xy - plane from the point with coordinates ( 0, 0 ) to any point on line a?
divide(multiply(100, 3), sqrt(add(power(4, const_2), power(3, const_2))))
this can be solve in two steps and without any complex calculation . given : equation of line a as y = ( 4 / 3 ) x - 100 . so the line intercept the axes at ( 0 , - 100 ) and ( 750 ) . this can be considered a right angle triangle with right angle at ( 00 ) . so base = 100 , height = 75 and hypotenuse = 125 ( by pythagoras triplet ) so a perpendicular from the ( 00 ) to hypotenuse will be the answer . area of triangle = 0.5 * 100 * 75 = 0.5 * 125 * x = > x = 60 ; so answer is 60 = c