Question

Find all points on the x axis that are 6 units from the point 4 3

Answer 1

use the distance formula

a point on the x axis is where y=0

disatnce formula
distance between (x1,y1) and (x2,y2) is

`D=√((x_2-x_1)^2+(y_2-y_1)^2)`

we have the point (4,3) and (x,0)
and D=6


`6=√((x-4)^2+(0-3)^2)`

`6=√(x^2-8x+16+(-3)^2)`

`6=√(x^2-8x+16+9)`

`6=√(x^2-8x+25)`
square both sides

`36=x^2-8x+25`
minus 36 both sides
0=x²-8x-11
factor
we can't
use quadratic formula
for
0=ax²+bx+c

`x=(-b+/-√(b^2-4ac))/(2a)`

so
0=1x²-8x-11
a=1
b=-8
c=-11


`x=(-(-8)+/-√((-8)^2-4(1)(-11)))/(2(1))`

`x=(8+/-√(64+44))/(2)`

`x=(8+/-√(108))/(2)`

`x=(8+/-6√(3))/(2)`

`x=4+/-3√(3)`

the 2 points are

`(4+3√(3),0) \space\ and \space\ (4-3√(3),0)`