Question

warm up!
segment jm has endpoints ( a(-5,1) ) and ( m(7,-9) ).
an equation of the perpendicular bisector of ( jm ) is

1. ( y - 4 = \frac { 5 } { 6 } ( x + 1 ) )
2. ( y - 4 = \frac { 6 } { 5 } ( x - 1 ) )
3. ( y + 4 = \frac { 6 } { 5 } ( x + 1 ) )

Explanation:

Step1: Find the mid - point of segment \(JM\)

The mid - point formula is \(M(\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})\). Given \(J(-5,1)\) and \(M(7,-9)\), then \(x=\frac{-5 + 7}{2}=1\), \(y=\frac{1+( - 9)}{2}=-4\). So the mid - point is \((1,-4)\).

Step2: Find the slope of segment \(JM\)

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Here, \(m_{JM}=\frac{-9 - 1}{7-( - 5)}=\frac{-10}{12}=-\frac{5}{6}\).

Step3: Find the slope of the perpendicular bisector

If two lines are perpendicular, \(m_1\times m_2=-1\). Let \(m_1 =-\frac{5}{6}\), then \(m_2=\frac{6}{5}\).

Step4: Use the point - slope form \(y - y_0=m(x - x_0)\)

We have \(m=\frac{6}{5}\) and the point \((x_0,y_0)=(1,-4)\). Substitute into the formula: \(y+4=\frac{6}{5}(x - 1)\)

Answer:

1. \(y + 4=\frac{6}{5}(x - 1)\)