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 (3, 4) and (-3, - 10) (x, y) = (smaller x-value) (x, y) = (larger x-value)

Solution

midpoint of (3, 4) and ( -3, -10) = (0, -3)

Lets assume apoint on x axis be ( x, 0)

Distance between (0, -3) and (x,0) = sqrt( (-3)^2 + x^2

sqrt( (-3)^2 + x^2) = 4 units

Taking square on both sides:

9 +x^2 = 16

x^2 = 7

x = +/-sqrt7

The points are ( sqrt7 , 0) and (-sqrt7 , 0)