Question

indicate the equation of the line, in standard form, that is the perpendicular bisector of the segment with endpoints (-1,6) and (5, 5). Enter your answer into the blank equation box.

Answer 1

The equation of the line, in standard form, that is the perpendicular bisector of the segment with endpoints (-1,6) and (5, 5) is 12x - 2y = 13.

In the question, we are asked to indicate the equation of the line, in standard form, that is the perpendicular bisector of the segment with endpoints (-1,6) and (5, 5).

The slope of the line with endpoints (-1,6) and (5,5), can be calculated as:

m = (6 - 5)/(-1 - 5) = 1/(-6) = -1/6.

Thus, the slope of the perpendicular bisector = -1/m = -1/(-1/6) = 6.

The perpendicular bisector passes through the midpoint of the line with endpoints (-1,6) and (5,5), which can be calculated as:

(x₁, y₁) = ( {(-1 + 5)/2},{(6 + 5)/2} ),

or, (x₁,y₁) = (2, 11/2).

Thus, the required equation can be shown as:

(y - 11/2) = 6(x - 2), which can be shown in the standard form as follows:

(2y - 11)/2 = 6x - 12,

or, 2y - 11 = 12x - 24,

or, 12x - 2y = 13.

Thus, the equation of the line, in standard form, that is the perpendicular bisector of the segment with endpoints (-1,6) and (5, 5) is 12x - 2y = 13.

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