## The distance of the point P on X-axis from point A(5, – 4) is 4 units. Then, the coordinates of P are ______________.

Question

The distance of the point P on X-axis from point A(5, – 4) is 4 units. Then, the coordinates of P are ______________.

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1 week 2021-10-04T15:41:40+00:00 2 Answers 0 views 0

P( 5 , 0 )

## SolutioN :

Condition :

• The distance of the point P on X-axis from point A is 4 units.
• When, y become 0.

Let,

• The point be Q( x , 0 )

So,

• A( 5 , – 4 )
• P( x , 0 )
• x1 = 5.
• x2 = – 4.
• y1 = x.
• y2 = 0.
• AP = 4 units.           Either,  Coordinates P( 5 , 0 )

### Therefore, the value of x is 5 units.

2. Let the point P which is on x – axis be ( x , 0 )

{ since on x axis y coordinate is zero }

Hence,

Distance,

AP = √ ( 0 + 4 )² + ( x – 5 )²

4 = √ 4² + x² + 25 – 10x

4² = 4² + x² – 10x + 25

x² – 10x + 25 = 0

x² – 5x – 5x + 25 = 0

x ( x – 5 ) – 5 ( x – 5 ) = 0

( x – 5 )² = 0

Hence x – 5 = 0

Implies x = 5

coordinates of P are ( 5 , 0 )

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