JEE Main202125 Feb 2021Morning ShiftMathematicsStraight LinesActual

The image of the point 3 , 5 in the line x - y + 1 = 0 , lies on :

Options

Ax - 2 2 + y - 4 2 = 4
Bx - 4 2 + y - 4 2 = 8
Cx - 4 2 + y + 2 2 = 16
Dx - 2 2 + y - 2 2 = 12

Correct answer

A. x - 2 2 + y - 4 2 = 4

Step-by-step solution

The slope of P P ' = - 1 ( As, P P ' is perpendicular to the given line) ⇒ k - 5 h - 3 = - 1   ⇒ k + h = 8     . . . 1 Mid-point of P P ' lies on the given line, ⇒ h + 3 2 - k + 5 2 + 1 = 0   ⇒   h + 3 - k - 5 + 2 = 0   ⇒   h - k = 0     . . . 2 Solving equation 1 and 2 we get, h = 4 ,   k = 4 Which satisfy the equation x - 2 2 + y - 4 2 = 4 .

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