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Question
A = (7, −2) and C = (−1, −6) are the vertices of square ABCD. Find the equations of diagonals AC and BD.
Solution
We know that in a square, diagonals bisect each other at right angle.
Let O be the point of intersection of the diagonals AC and BD.
Co-ordinates of O are
`((7 - 1)/2, (-2 - 6)/2) = (3, -4)`
Slope of AC = `(-6 + 2)/(-1 - 7) = (-4)/-8 = 1/2`
For line AC:
Slope = m = `1/2`, (x1, y1) = (7, –2)
Equation of the line AC is
y – y1 = m(x – x1)
`y + 2 =1/2 (x - 7)`
2y + 4 = x – 7
2y = x – 11
For line BD:
Slope = m = `(-1)/("slope of AC") = (-1)/(1/2)= -2`,
(x1, y1) = (3, −4)
Equation of the line BD is
y − y1 = m(x − x1)
y + 4 = −2(x − 3)
y + 4 = −2x + 6
2x + y = 2
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