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Answers
Answer❣
Given
We have given two points M( -5,-2) and N( 3,2)
To find
we have to find the point on x - axis which is equidistant from the points M and N
Solution,
since ,we don't know the points let us assume the point on x axis be ( x,0)
Note : On x-axis the y will be zero and on Y-axis x will be zero.
let x be 'a'
so , our new point be P (a,0)
According to the questio:
If the point P is equidistant from M and N
then their distance between the points PM and PN must be equal.
Now, by using distance formula we will find distance between the two points.
Distance Between P and M
Distance formula
D=√(x₂- x₁)²+(y₂- y₁)²
M( -5,-2) and P(a,0)
x₁= -5 ;x₂ = a ; y₁= -2 & y₂ = 0
PM= √ (a+5)²+(0+2)²
identity :(a+b)²= a²+b²+2ab
PM= √ a²+5²+2(a)(5)+2²
PM= √a²+25+10a+4=√ a²+10a+29
Distance between P and N
P(a,0) N ( 3,2)
PN=√ (3-a)²+(2-0)²
PN= √ 9+a²-6a+4= √ a²-6a+13
Now , comparing both PM and PN
√ a²+10a+29=√a²-6a+13
Squaring both sides
PM²= PN²
(√a²+10a+29)²= (√a²-6a+13)²
a²+10a+29=a²-6a+13
a² gets cancelled as base same
=> 10a +29= -6a+13
=> 10a+6a=13-29
=> 16a = -16
=>a = -1
Thus,the point is (a,0) = (-1,0)
Therefore, (-1,0) is the point on the x-axis which is equidistant from the points M