Question

What is the value of at the points (35) and (7.1) are equidistant from the point (a,0)​

Answer 1

Answer:

Here we go…………

Locus of a poiny equidistant from the given two points will be a straight line..

If we somehow able to find the equation of this line then finding ‘a’ would be a easy job…

Now think carefully …..the line perpendicular to the line joinging (3,5)&(7,1) is the required locus of points equidistant from two (3,5)&(7,1).

Let us call line joining (3,5)&(7,1)=> Ľ

And line joining (3,5)&(7,1) => Ļ

For verification : this line Ļ passes through mid point of the points (3,5)&(7,1)…

Now mid point (X,Y)between (3,5)&(7,1) can be given by mid point formula

X=(3+7)/2= 5

Y=(5+1)/2=3

Also slope of line joining (3,5)&(7,1) i.e Ľ=(5-1)/(3-7) =-1

Therefore slope of line perpendicular to line joining (3,5)&(7,1) i.e Ļ=1

Now we have a point and slope of line Ļ=> we can find equation of line using slope point form of line.

Equation of line => (y-Y)=m (x-X)….

(y-3)=1(x-5) or y=x-2

Putting point (a,0) in above line

0=a-2

=> a=2

I hope its help you.