Exploring Diagonals in a Square: Finding the Equation of Diagonal BD

In a square, the diagonals not only bisect each other, but they are also equal in length and at a 90-degree angle to each other. If we look at the line AC represented by the equation: 3x+2y-7=0, we find that the slope of this line (m1) is -3/2. Since the diagonals are perpendicular to each other, the slope of the line BD (m2) should be negative reciprocal of m1. That gives us m2 = 2/3. Using the point slope form of a line equation, y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point (3, 5) on the line BD, we find: y - 5 = 2/3 (x - 3) Multiplying through by 3 to clear the fraction gives: 3y - 15 = 2x - 6 Rearranging terms gives the equation of the line BD as: 2x - 3y + 9 = 0.