Identify the equation in point-slope form for the perpendicular bisector of the segment with endpoints J(−24,−4) and K(−4,6). Option A:

y + 6 = 2(x − 4)

Option B:

y − 6 = 2(x + 4)

Option C:

y + 1 = −2(x − 14)

Option D:

y − 1 = −2(x + 14)

Given:

Endpoints of a segment are J(−24,−4) and K(−4,6).

To find:

The equation in point-slope form for the perpendicular bisector of JK.

Solution:

Slope of JK is

Product of slopes of two perpendicular lines is -1. So, product of perpendicular line of JK is -2.

Perpendicular bisector of JK passes through the midpoint of JK.

Point slope form:

where, m is slope.

Perpendicular bisector of JK passes through (-14,1) with slope -2. So, the point slope form of JK is

Therefore, the correct option is D.