Question

if the distance between two points (x,7)and(1,15)is10 find the value of x

Answer 1

Say (x1,y1) = (x,7)

(x2,y2) = (1,15)

Distance between two points = √[(x2-x1)^2+(y2-y1)^2]

10 = √[(1-x)^2+(15-7)^2

10 = √(1+x^2-2x+64)

10 = √(x^2-2x+65)

Squring to each side.

100 = x^2-2x+65

Bring all terms to one side.

x^2-2x+65-100 = 0

x^2-2x-35 = 0

x^2-7x+5x-35 = 0

x(x-7)+5(x-7) = 0

(x+5)+ (x-7) = 0

x+5 = 0 and x-7 = 0

x = -5 and x = 7