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If (−4, 7) is one vertex of a rhombus and if the equation of one diagonal is 5x − y + 7 = 0, then find the equation of another diagonal

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#### Solution

In a rhombus

The diagonal cut at right angles.

The given diagonal is 5x – y + 7 = 0 and (– 4, 7) is not a point on the diagonal.

So it will be a point on the other diagonal which is perpendicular to 5x – y + 7 = 0.

The equation of a line perpendicular to 5x – y + 7 = 0 will be of the form x + 5y + k = 0.

It passes through (– 4, 7)

⇒ – 4 + 5(7) + k = 0

⇒ k = – 31

So the equation of the other diagonal is x + 5y – 31 = 0

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