Answer:
Explanation:
Find the midpoint of the segment by using the formula [(x1 + x2)/2, (y1 + y2)/2]. The midpoint is [(2 + 6)/2, (1 + 3)/2] = (4, 2).
Find the slope of the segment by using the formula (y2 - y1)/(x2 - x1). The slope is (3 - 1)/(6 - 2) = 1/2.
Find the negative reciprocal of the slope by flipping the fraction and changing the sign. The negative reciprocal is -2/1 or -2.
Find the equation of the perpendicular bisector by using the point-slope form y - y1 = m(x - x1), where m is the negative reciprocal and (x1, y1) is the midpoint. The equation is y - 2 = -2(x - 4).
Simplify the equation by distributing and rearranging. The equation is y = -2x + 10. This is the equation of the perpendicular bisector in slope-intercept form.