What is the perpendicular bisector equation of the line joined by the points 11 13 and 17 19 showing work and answer?

Answer 1

The equation of a line through point (x0, y0) with gradient m is given by:

y - y0 = m(x - x0)

The gradient (m) of a line between two points (x0, y0) and (x1, y1) is given by:

m = change_in_y/change_in_x = (y1 - y0)/(x1 - x0)

→ The equation of the line between (11, 13) and (17, 19) is given by:

y - 13 = (19-13)/(17-11) (x - 11)

→ y - 13 = 6/6 (x - 11)

→ y - 13 = x - 11

→ y = x + 2

and its gradient is m = 1.

The gradient (m') of a line perpendicular to a line with gradient m is such that mm' = -1, ie m' = -1/m

→ The gradient of the perpendicular line to the line between (11, 13) and (17, 19) has gradient m' = -1/1 = -1.

The perpendicular bisector goes through the point midway between (11, 13) and (17, 19) which is given by the average of the x and y coordinates: ((11+17)/2, (13+19)/2) = (14, 16)

Thus the perpendicular bisector of the line joining (11, 13) to (17,19) is given by:

y - 16 = -1(x - 14)

→ y - 16 = -x + 14

→ y + x = 30

Which in its general form is: x+y-30 = 0