Find the equation of the perpendicular bisect | vedclass

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Question

(A) The perpendicular bisector of the line segment joining points $A(3,4)$ and $B(-1,2)$ passes through the midpoint of $AB$ and is perpendicular to t

Vedclass · Accepted Answer

$2x + y - 5 = 0$

Vedclass · Answer

(A) The perpendicular bisector of the line segment joining points $A(3,4)$ and $B(-1,2)$ passes through the midpoint of $AB$ and is perpendicular to the line segment $AB$. First,find the midpoint $M$ of $AB$: $M = \left(\frac{3 + (-1)}{2}, \frac{4 + 2}{2}\right) = \left(\frac{2}{2}, \frac{6}{2}\right) = (1, 3)$. Next,find the slope of line segment $AB$: $m_{AB} = \frac{2 - 4}{-1 - 3} = \frac{-2}{-4} = \frac{1}{2}$. The slope of the perpendicular bisector $(m_{\perp})$ is the negative reciprocal of $m_{AB}$: $m_{\perp} = -\frac{1}{m_{AB}} = -\frac{1}{1/2} = -2$. Using the point-slope form $y - y_1 = m(x - x_1)$ with point $(1, 3)$ and slope $-2$: $y - 3 = -2(x - 1)$ $y - 3 = -2x + 2$ $2x + y - 5 = 0$. Thus,the correct option is $A$.

Find the equation of the perpendicular bisector of the line segment joining the points $(3,4)$ and $(-1,2)$.

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