Question

Need help ASAP!

Write a formula for the distance from A (-1, 5) to P (x, y), and another formula for the distance from P (x, y) to B (5, 2). Then write an equation that says that P is equidistant from A and B. Simplify your equation to linear form. This line is called the perpendicular bisector of AB. Verify this by calculating two slopes and one midpoint.

Thanks!

Answer 1

Explanation:

A=(-1,5)

B=(5,2)

P=(x,y)

AP²=(x+1)²+(y-5)²=x²+2x+1+y²-10y+25

BP²=(x-5)²+(y-2)²=x²-10x+25+y²-4y+4

AP²=BP² ==> 12x-6y=3 or y=2x-1/2

Proof:

`AB\ slope=\frac{2-5 } { 5+1 } =-\frac { 1 } { 2 } \\\\perpendicular\ slope =2\\\\middle\ of\ AB=(2, (7)/(2) )\\\\perpendicular\ bisector:\ y-(7)/(2) =(x-2)*2\\\\y=2x-(1)/(2) \\\\`