Question

Please guys answer fast

Answer 1

AnsWer :

( - 2 , 0 )

QuestioN :

Find the coordinates of the point on X - axis Which is equidistant from point p ( - 2 , 5 ) and Q( 2 , - 3 ).

SolutioN :

• P( - 2 , 5 )
• Q( 2 , - 3 )
• A( x , y )
• A( x , 0 )

$\tt \dagger \: \: \: \: \: PA = QA$

$\tt \longmapsto \sqrt{{(x + 2) }^{2} + {(0 - 5)}^{2} } = \sqrt{ {(x - 2)}^{2} + {(0 + 3)}^{2} }$

$\tt \longmapsto \sqrt{{x }^{2} + 4 + 2x+ 25 } = \sqrt{ {x}^{2} + 4 - 2x+ 9}$

$\tt \longmapsto {x }^{2} + 4 + 4x+ 25 = {x}^{2} + 4 - 4x+ 9$

$\tt \longmapsto 4x+ 25 =- 4x+ 9$

$\tt \longmapsto 8x+ 25 =9$

$\tt \longmapsto8x = - 16.$

$\tt \longmapsto x = - \dfrac{16}{8}$

$\tt \longmapsto x = - 2.$

Therefore, the point Where, P and Q equidistant be A( - 2 , 0 )

Answer 2

Answer:

Step-by-step explanation:

Given,

As the point is on the x axis, we can assume the coordinate of the point as (x,0)

Distance Formula = $\sqrt{(x_{2} - x_{1})^2 + (y_2 -y_1)^2 }$

Now,

$\sqrt{(x+2)^2 + (0-5)^2} = \sqrt{(x-2)^2+(0-3)^2}$

S.B.S,

$or,x^2 + 4x + 4 +25 = x^2-4x+4+9\\or,4x+25=-4x+9\\or,8x=-16\\or,x=-2$

∴Hence the point is (-2,0) which is equidistant from (-2,5) and (2,-3)