Question

if p(x,y) is equidistant from the points A(7,-2) and B(3,1) express y in terms of x

Answer 1

p will lie on a line passing through midpoint of AB and perpendicular to it
let M is mid point M (5,-1/2)
slope of tht line will be -1/slope of AB
using slope point form write equation of line

Answer 2

Answer:

The expression required of y in terms of x is $y=\frac{8x-43}{6}$

Step-by-step explanation:

Given : If p(x,y) is equidistant from the points A(7,-2) and B(3,1).

To express : y in terms of x?

Solution :

Since, point p is equidistanhce from point A and B

i.e, The distance between AP=BP

Applying distance formula between them,

i.e, $d=\sqrt{(x-x_1)^2+(y-y_1)^2}$

Point A(7,-2), p(x,y) and B(3,1)

Distance of AB=Distance of BP

$\sqrt{(7-x)^2+(-2-y)^2}=\sqrt{(3-x)^2+(1-y)^2}$

Cancel the square both side,

$(7-x)^2+(-2-y)^2=(3-x)^2+(1-y)^2$

Opening the square both side,

$49+x^2-14x+4+y^2+4y=9+x^2-6x+1+y^2-2y$

$49-14x+4+4y=9-6x+1-2y$

$-14x+6x+4y+2y=9-49-4+1$

$-8x+6y=-43$

$6y=-43+8x$

$y=\frac{8x-43}{6}$

Therefore, The expression required of y in terms of x is $y=\frac{8x-43}{6}$