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