Mathematics: Determine the equation of the perpendicular bisector JK whose endpoints are J(-4,9) and K(6,1). Show all your work below. (Use of the grid is optional.)

Determine the equation of the perpendicular bisector

gandalfhan

09.02.2022

$y=\frac{5}{4}x+\frac{15}{4}$

Step-by-step explanation:

Coordinates of segment with endpoints J and K are,

J(-4, 9) and K(6, 1)

Midpoint of the segment JK = $(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

= $(\frac{-4+6}{2},\frac{9+1}{2})$

= (1, 5)

Slope of JK, $(m_1)=\frac{y_2-y_1}{x_2-x_1}$

= $\frac{9-1}{-4-6}$

= $-\frac{4}{5}$

Let the equation of perpendicular bisector passing through (x_1,y_1) and slope m_2 is,

y-y_1=m_2(x - x_1)

By the property of perpendicular lines,

$m_1\times m_2=-1$

$-\frac{4}{5}\times m_2=-1$

$m_2=\frac{5}{4}$

Therefore, equation of the line passing through midpoint (1, 5) and slope = $\frac{5}{4}$ will be,

$y-5=\frac{5}{4}(x-1)$

$y=\frac{5}{4}x-\frac{5}{4}+5$

$y=\frac{5}{4}x+\frac{15}{4}$

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