Question

the given line segment has a midpoint at (-1, -2). what is the equation, in slope-intercept form, of the perpendicular bisector of the given line segment?
options:
( y = -4x - 4 )
( y = -4x - 6 )
( y = \frac{1}{4}x - 4 )
( y = \frac{1}{4}x - 6 )
(graph shows points (-5, -3), (-1, -2), (3, -1) on a coordinate plane)

Explanation:

Step1: Find slope of given segment

Using points \((-5, -3)\) and \((3, -1)\), slope \(m = \frac{-1 - (-3)}{3 - (-5)} = \frac{2}{8} = \frac{1}{4}\).

Step2: Find slope of perpendicular bisector

Perpendicular slope is negative reciprocal: \(m_{\perp} = -4\).

Step3: Use midpoint to find equation

Midpoint \((-1, -2)\), use point - slope form \(y - y_1 = m(x - x_1)\):
\(y - (-2) = -4(x - (-1))\)
\(y + 2 = -4(x + 1)\)

Step4: Simplify to slope - intercept form

\(y + 2 = -4x - 4\)
\(y = -4x - 6\)

Answer:

\(y = -4x - 6\) (corresponding to the option \(y = -4x - 6\))