The points B(2, 6) and D(0, -2) are two opposite vertices of a square ABCD, find the equation of the diagonal AC.

y = -x/4 + 9/2

Step-by-step explanation:

The diagonal AC is the perpendicular bisector of BD.

The centre of the square, P, through which both diagonal pass through is at the average of the coordinates of B(2,6) and D(0,-2)

P ((2+0)/2, (6-2)/2) = P(1,2)

The slope of BD,

m = (yd-yb)/(xd-xb) = (-2-6)/(0-2) = -8/-2 =4

Slope of AC

m' = -1 / m = -1/4

Using the point slope form of the line AC, slope m' through P(1,2)

y-yp = m'(x-xp)

y-2 = -(1/4)(x-1)

Simplify and isolate y

y = -x/4 + 1/4 +2 = -x/4 + 9/2