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Question
ABCD is a square. The cooordinates of B and D are (-3, 7) and (5, -1) respectively. Find the equation of AC.
Solution
Slope of BD = `(7 + 1)/(-3 -5)` = 1
Slope of AC = 1
Mid point of AC = mid point of BD
O(x,y) = `((5 - 3)/2 , (-1 + 7)/2)` = (1,3)
Equation of AC ⇒ `("y" - "y"_1)/("x" - "x"_1)` = slope
⇒ `("y" - 3)/("x" - 1) = 1`
⇒ x - 1 = y - 3
⇒ x - y + 2 = 0
⇒ y = x + 2
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