Question

please solve 13..…...

Answer 1

let ( a, 0) and ( 0, b) are the points lies on axes .
a/c to question,

( a , 0) -----------(3, 5) ----------(0, b)

use section formula , for midpoint
3 = ( a + 0)/2

a = 6

and 5 = (0 + b)/2
b = 10

now , ( 6, 0) and (0, 10) are two points on axes .
so ,equation of line is
( y -0) = (10-0)/(0-6)( x -6)

y = -5/3 ( x -6)

3y +5x - 30 = 0

and distance from origin =|30|/√34

Answer 2

Let the line intersect X-axis at point (0,a) & y-axis at (b,0)

According to the question;
the line is bisected at the point (3,5)

hence (3,5) is the midpoint of the line joining points (0,a) & (b,0)

3 = (0+b)/2
5 = (a+0)/2

a = 10 & b = 6

Hence the line is passing through points (0,10) , (6,0)

Equation of the line is;

y-10 = [(0-10)/(6-0)] (x-0)
y-10 = -(5/3) x
3y-30 = -5x

5x+3y-30 = 0
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Distance of the line from the origin (0,0) is

= (-30)/√(5²+3²)
= 30/√34 units