The line represented by the equation $y = - 2 x + 6$ is the perpendicular bisector of the line segment AB. If A has the coordinates (7,2), what are the coordinates for B ?

(3, 0)

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(4, 0)

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(6, 2)

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(5, 6)

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Solution

The correct option is A $(3, 0)$
Given line
$y = - 2 x + 6$
On comparing above equation with $y = m x + c$
$m = - 2$
The slope of perpendicular line to line $y = - 2 x + 6$
$m_{1} m = - 1$
$m_{1} (- 2) = - 1$
$m_{1} = \frac{1}{2}$
The equation of line with slope $m_{1}$ and Point $A (7, 2)$
$y - 2 = \frac{1}{2} (x - 7)$
$2 y - 4 = x - 7$
$x - 2 y = 3$
Let Point B $(x_{1}, y_{1})$
Point B lies on $x - 2 y = 3$
$x_{1} - 2 y_{1} = 3$
On putting $y_{1} = 0$
$x_{1} = 3$
Point $B (3, 0)$

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The line represented by the equation y=−2x+6 is the perpendicular bisector of the line segment AB. If A has the coordinates (7,2), what are the coordinates for B ?

The line represented by the equation $y = - 2 x + 6$ is the perpendicular bisector of the line segment AB. If A has the coordinates (7,2), what are the coordinates for B ?