Find all points on the xaxis that are 4 units from the midpo

Find all points on the x-axis that are 4 units from the midpoint of the line segment joining

(1, 4) and (1, 10).

(x,y) ______ (smaller x-value)

(x,y) ______ (larger x-value)

Solution

midpoint of the line segment joining (1, 4) and (1, 10).

m=((1-1)/2, (4-10)/2)

m=(0,-3)

let point on x axis be p(x,0)

ditance betwwn midpoint m and  point on x axis p(x,0) =4 units

[(x-0)²+(0-(-3))²] =4

x²+9 =4²

x²=16 -9

x²=7

x=-7 , x=7

(x,y) _(-7,0)_ (smaller x-value)

(x,y) _(7,0)_ (larger x-value)