Question

Find the point on x axis equidistant from (2, -3) and (3, 5)

Answer 1

Answer:

2 and 3

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Answer 2

Step-by-step explanation:

Given:-

Find the point on x axis equidistant from (2, -3) and (3, 5).

To find:-

Find the point on x axis equidistant from (2, -3) and (3, 5)

Solution:-

Let the point on x -axis =(x,0)

Since the point on x-axis is y=0

Given points are (x1,y1)=(2,-3)

=>x1=2 and y1=-3

and (x2,y2)=(3,5)=>x2=3,y2=5

Using formula:-

Distance between the two points (x1,y1) and(x2,y2) is

√[(x2-x1)²+(y2-y1)²] units

A(2,-3).__________.P(x,0)_________.B(3,5)

Distance between A and P

=>√[(x-2)²+(0+3)²]

=>√(x²-4x+4+9)

AP=√(x²-4x+13) ----(1)

Distance between P and B

=>BP=√[(3-x)²+(5-0)²]

=>Bp=√(9+x²-6x+25)

BP=√(x²-6x+34) -------(2)

according to the given problem

(1)=(2)

=>√(x²-4x+13)=√(x²-6x+34)

On squaring both sides

=>x²-4x+13=x²-6x+34

=>-4x+13=-6x+34

=>-4x+6x=34-13

=>2x=21

=>x=21/2

P(21/2,0)

Answer:-

The coordinates of point is (21/2,0)