What is the equation and its perpendicular bisector equation of the line that joins the points of 3 7 and 5 9 on the Cartesian plane showing work?

Answer 1

Let P = (3, 7) and Q = (5, 9)

Then gradient of PQ, m1 = (9 - 7)/(5 - 3) = 2/2 = 1

So equation of PQ: (y - yQ) = m1*(x - xQ)

or y - 9 = 1*(x - 5) => x - y + 4 = 0

Midpoint of PQ: R = [(3+5)/2, (7+9)/2] = (4, 6)

Gradient of perpendicular bisector, m2 = -1/m1 = -1

So equation is (y - yR) = -1*(x - xR)

or y - 6 = -1*(x - 4) => x + y - 10 = 0

Slight Correction:-

Midpoint: (3+5)/2 and (7+9)/2 = (4, 8)

Perpendicular equation: y-8 = -1(x-4) => y = -x+12 or as x+y-12 = 0