Question

Find the point (x,y)
on the line y = x that is equidistant from the points (-6,2) and (10,-9)​

Answer 1

(14.1, 14.1)

Explanation:

If the point (x,y) is on the line y=x, then it has coordinates (x,x).

Find the distances from this point to points (-6,2) and (10,-9):

• distance from (x,x) to (-6,2):
  `√((x-(-6))^2+(x-2)^2)=√((x+6)^2+(x-2)^2)`
• distance from point (x,x) to (10,-9):
  `√((x-10)^2+(x-(-9))^2)=√((x-10)^2+(x+9)^2)`

Equate these distances:

`√((x+6)^2+(x-2)^2)=√((x-10)^2+(x+9)^2)`

Square this equation:

`(x+6)^2+(x-2)^2=(x-10)^2+(x+9)^2\\ \\x^2+12x+36+x^2-4x+4=x^2-20x+100+x^2+18x+81\\ \\8x+40=-2x+181\\ \\8x+2x=181-40\\ \\10x=141\\ \\x=14.1`

So, the coordinates are (14.1, 14.1)