Question

the point equidistant from the lines x+y=1 ,y=1 and x=1 is

Answer 1

Answer:

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Answer 2

Answer:

Step-by-step explanation:

TIP:

A point equidistant from two or more lines means the distance between the point from the two or more lines are same or equal.

GIVEN:

• line1 :$x+y-1=0$
• line 2: $y=1$
• line 3: $x=1$

TO FIND:

     a point equidistant from all the three given lines

EXPLANATION:

Let's assume the point equidistant to all three lines be (a , b).

Distance of a point from a line  $fx+gy+h=0$  is  $\frac{|fa+gb+h|}{\sqrt{f^{2}+g^{2} } }$

So, the distance of the point(a, b) from line1 is

$\frac{|a+b-1|}{\sqrt{1^{2}+1^{2} } }$

⇒$a+b-1$

Distance of a point from line $y=1$ is $|b-1|$

Distance of a point from line $x=1$ is $|a-1|$

As the point is equidistant from the three lines,

$a+b-1 = b-1$ ..................................................(1)

$a+b-1 = a-1$ ..................................................(2)

Now, by solving equation 1, we get

$a=0$

And by solving equation 2, we get

$b=0$

Therefore the point equidistant to all the three lines is (0,0).

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