The points A(4,0), B (4,4), C (0,4) and D (0,0) form a square. Find the slopes of BD and AC. What does your results say about the diagonals BD and AC?
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Given in the question that the points A(4,0), B (4,4), C (0,4) and D (0,0) form a square .
The two diagonals of the square are BD and AC.
The slope of the diagonal BD = m1 = (0-4)/(0-4) = 1
The slope of the diagonal AC = m2= (4-0)/(0-4) = -1
=> m1 × m2 = -1
The length of diagonal BD = √(16+16) = √32
Length of the diagonal AC = √(16+16) = √32
From the results we get that the two diagonals are perpendicular to eachother as the product of their slopes is equal to -1.
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