Question

Which equation represents the perpendicular bisector of the segment with endpoints B(6,9) and C(8,−7)?

A) y − 7 = 8(x − 1)
B) y−1=−18(x−7)
C) y−1=18(x−7)
D) y − 1 = −8(x − 7)

Answer 1

The equation that represents the perpendicular bisector of the segment with endpoints B(6,9) and C(8,−7) is C) y−1=18(x−7).

Step-by-step explanation:

The equation that represents the perpendicular bisector of the segment with endpoints B(6,9) and C(8,−7) is y−1=18(x−7).

To find the equation of the perpendicular bisector, we first need to find the midpoint of the segment BC. The midpoint is calculated by taking the average of the x-coordinates and the average of the y-coordinates. In this case, the midpoint is M((6+8)/2, (9+(-7))/2) = M(7,1).

The slope of the line BC is (−7−9)/(8−6) = -16/2 = -8. The slope of the perpendicular bisector is the negative reciprocal of -8, which is 1/8.

Using the point-slope form of the equation y−y1=m(x−x1), we can plug in the values of M(7,1) and m=1/8 to obtain the equation y−1=1/8(x−7). This can be simplified to y−1=18(x−7).