Question

find the value of x, if the distance between the points (x, -1) and (3,-2) is x+5.

Answer 1

The distance between two points
= √(x2-x1)^2 + (y2-y1)
where the two points are (x1,x2) & (y1,y2)

Here ;
the points are (x,-1) & (3,-2)
x1 = x
x2 = 3
y1 = -1
y2 = -2
and the distance between this two points is x+5.
Using the distance formula we get ;

x+5 = √(3-x)^2+(1-2)^2
squaring both sides
(x+5)^2 = (3-x)^2 +1
x^2+25+10x = 9+x^2-6x +1

25-9-1 = -16x
15 = -16x
x = 15/-16

Answer 2

let A(x, -1) and B(3,-2)
AB =x+5
AB²= (x+5)²

(3-x)²+[-2-(-1)]²=(x+5)²
(3-x)²+(-2+1)²=(x+5)²
9-6x+x²+1=x²+10x+25
⇒x²-x²-6x-10x=25-1-9
⇒-16x=15
x= -15/16