Question

The equation of straight line which bisect the intercept made by the axis on the line x+y=2 and 2x+3y=6

Answer 1

Solution :-

First of all , we will find x- intercept and y - intercept of x + y = 2

So when we will plug x = 0 in the equation then we get y = 2 . So we have ( 0 ,2 ) y- intercept )

And when we will plug y = 0 then we get x = 2 . So we have ( 2, 0) x- intercept )

Now we have to find midpoint from (0,2) and ( 2, 0)

Mid point formula x = (x1 + x2) / 2 = 0 + 2 / 2 = > 2/2 = > 1

Also y = ( y1+ y2)/ 2 = 2+0 / 2 = > 2/2 = > 1

So mid points are ( 1, 1)

Now from second equation we will find x- intercept and y - intercept (2x+3y = 6)

When we will plug x =0 then we get y = 2 , So we have ( 0, 2) --- y-intercept

And when we will plug y = 0 then we get x = 3 , So we have ( 3, 0) - -- x-intercept


So we will find the mid points from (0,2) ( 3,0 )

x = 0 + 3/ 2 = > 3/ 2

y = 2+0 / 2 = > 2/2 = > 1

So mid points are ( 3/2 , 1)

Now we have two co-ordinates ( 1,1 ) and ( 3/2 , 1)

So we will find slope , formula slop (m) = y2- y1 / x2- x1

= (1 - 1) / (3/2 - 1 )

= 0 / ( 1/2)

So we got slope = 0

Now we will apply slope point form , formula = y - y1 = m ( x- x1 )

So slope (m) = 0 , x1 = 1 and y1 = 1 ( we can choose any one co-ordinate )

Now we will plug the values in the formula.

Therefore , y - 1 = 0 ( x- 1 )

= > y - 1 = 0

=> y = 1 That would be the final answer.