Question

Find the value of m such that the point P(0,m) is equidistant from (5,3) and B(0,5)​

Answer 1

$\huge\star{\green{\underline{\mathfrak{Answer :-}}}}$

If the point P is equidistant from the other two points let A and B.

So, the point P is actually the midpoint of other two points.

We need to find the y coordinate of the midpoint.

So, we will use the midpoint formula for y coordinate that is :- $\dfrac {y_1+y_2}{2}$.

Let us substitute the values,

$=\dfrac {3+5}{2}$

$=\dfrac {8}{2}$

$= 4$

So, the value of m or the y coordinate of the point P is 4.

_____________

Answer 2

Question

Find the value of m such that the point P(0,m) is equidistant from (5,3) and B(0,5)

Solution

Let the given points be A(5,3) and B(0,5)

P is equidistant from points A and B » PA = PB

To find

Value of m

Using Mid Point Formula,

$\tt{p(0 \: m) = p( \dfrac{x {}_{1} + {x}_{2} }{2} \: \dfrac{ {y}_{1} + {y}_{2} }{2}) }$

Now,

$\large{ \sf{m = \dfrac{3 + 5}{2} }} \\ \\ \large{ \implies \: \boxed{ \boxed{ \sf{m = 4}}}}$

Thus,the midpoint of AB would be (0,4)