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Question
ABCD is rhombus. The coordinates of A and C ae (3,7) and (9,15). Find the equation of BD.
Solution
Diagnols of a rhombus bisect each other
`therefore` mid point of BD = mid point of AC
= `"O"((3 + 9)/2 ,(7 + 15)/2)`
= O (6,11)
Slope of AC = `(15 - 7)/(9 - 3) = 8/6 = 4/3`
Slope of BD = `-1/"Slope of AC" = (-3)/4`
Equation of BD is, `("y" - "y"_1)/("x" - "x"_1)` = Slope
`("y" - 4)/("x" - 6) = (-3)/4`
⇒ -3x + 18 = 4y - 44
⇒ x + 4y = 62
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