Question

find the coordinates of a point on y axis which is equidistant from M(-5,-2) and N(3,2).

Answer 1

Answer:

the coordinates of a point on y axis which is equidistant from M(-5,-2) and N(3,2). = (0.-2)

Step-by-step explanation:

Let coordinate which is required to find be X

Since the coordinates of point which is required to find lies on y axis so x coordinate will be 0 and let y coordinate be b

So, coordinate of that point = (0,b)

Distance between X and M

We will use distance formula :

$d=\sqrt{(x_{2} -x_{1})^{2} +(y_{2}-y_{1} )^{2}$

Coordinates of X = $(x_{1} ,y_{1} )=(0,b)$

Coordinates of M = $(x_{2} ,y_{2} )=(-5,-2)$

Putting values in distance formula ":

$d=\sqrt{(-5-0)^{2} +(-2-b)^{2}}$ --a

now to find distance between X and N

Coordinates of X = $(x_{1} ,y_{1} )=(0,b)$

Coordinates of N = $(x_{2} ,y_{2} )=(3,2)$

Putting values in distance formula ":

$d=\sqrt{(3-0)^{2} +(2-b)^{2}}$ -b

now since we are given that X must be equidistant from M and N

⇒equation a = equation b

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

⇒$25+(-2-b)^{2} =9+(2-b)^{2}$

⇒$25-9+(-2-b)^{2} =(2-b)^{2}$

⇒$16+4+b^{2}+4b =4+b^{2}-4b$

⇒$16+4b =-4b$

⇒$16 =-4b-4b$

⇒$16 =-8b$

⇒$b=-\frac{16}{8}$

⇒$b=-2$

Thus  the coordinates of a point on y axis which is equidistant from M(-5,-2) and N(3,2). = (0.-2)