A point P os equi distant from R(-2,4) and S(6,-4) and its x co ordinate is twice its Y co ordinate find co ordinates of P

Step-by-step explanation: Distance between two points is calculated as

Equidistant means the same distance, i.e., the distance between points P and R is equal to the distance between points P and S.

Suppose P's y-coordinate is a. If its x-coordinate is double, then

(x,y) = (2a,a)

Thus

Solving

y-coordinate is , then x-ccordinate is

2a = 2(-2) =

Coordinates of point P equidistant for R and S is .

fwms@lil_ben06

step-by-step explanation:

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1