A line segment with length 65 has one endpoint at (3, 9) . The other endpoint is at (-4, y) . Determine a value of y.

Length of a line connecting two points (x1, y1) and (x2, y2) is given by

Length = [x2 - x2)^2 + (y2 - y1)^2]^1/2

Substituting the coordinates of the two given points in the above formula, we get the length of given line as:

Length = [(-4 - 3)^2 + (y -9)^2]^1/2

= [(-7)^2 + (y - 9)^2]^1/2

= [49 + (y - 9)^2]^1/2

As length of the line is given to be equal to 65:

[49 + (y - 9)^2]^1/2 = 65

squaring both sides of the equation we get

49 + (y - 9)^2 = 4225

(y - 9)^2 = 4225 - 49 = 4176

y - 9 = 4176^(1/2)

y - 9 = 64.622 or (-64.622)

Taking positive value of 4176^(1/2)

y - 9 = 64.622

y = 64.622 + 9 = 73.622

Taking negative value of 4176^(1/2)

y - 9 = - 64.622

y = -64.622 + 9 = - 55.622