Question

if the point (x,y) is equidistant from the points (-3,-3) and (5,5), show that x any y satisfy the equation x+y=2. HELP!!!

Answer 1

The midpoint of (-3,-3) and (5,5) is (1,1).
The slope of the line from (-3,-3) to (5,5) is 1.
The slope of the perpendicular to the line from (-3,-3) to (5,5) is -1
What is the equation of the perpendicular bisector of the segment going from your two points?

Answer 2

let (x,y) be point equidistant from two points
then find d from both the points equate the two,square both sides and simplify

Answer 3

y= -x + b
b=2
y + x =2

Answer 4

The equation of the perpendicular bisector is therefore y=-x+2

Answer 5

Since it goes thru (1,1)

Answer 6

and has slope -1

Answer 7

\[\sqrt{\left( x+3 \right)^2+\left( y+3 \right)^2}=\sqrt{\left( x-5 \right)^2+\left( y-5\right)^2}\]
square and simplify
\[x^2+2x+9+y^2+6y+9=x^2+10y+25+y^2+10y+25\]
\[6x+6y+18=10x+10y+50,16x+16y=32,x+y=2\]