The points (2, 5) and (6, 3) are two end points of a diagonal of a rectangle

• Geometry

The points (2, 5) and (6, 3) are two end points of a diagonal of a rectangle. If the other diagonal has the equation y = 3x + c, then c is

1. -5
2. -6
3. -7
4. -8

Answer

In a rectangle, diagonals bisect each other, so one diagonal should pass through the midpoint of the other.

Midpoint of the diagonal connecting (2, 5) and (6, 3)

= [(2+6)/2, (5+3)2] = (4, 4)

The other diagonal, y = 3x + c should also pass through (4, 4).

On substitution,

4 = 3(4) + c

c = -8

The correct option is D.