Final answer:
The equation of the perpendicular bisector of dt is y - 3 = -2(x - 4).
Step-by-step explanation:
To find the equation of the perpendicular bisector of DT, we first need to find the midpoint of the segment DT.
The midpoint is the average of the x-coordinates and the average of the y-coordinates of the endpoints.
In this case, the midpoint is ((2+6)/2, (2+4)/2) = (4, 3).
Next, we need to find the slope of DT.
The slope of a line passing through two points (x1, y1) and (x2, y2) is given by (y2-y1)/(x2-x1).
In this case, the slope of DT is:
(4-2)/(6-2)
= 2/4
= 1/2.
The slope of the perpendicular bisector of DT is the negative reciprocal of the slope of DT.
So, the slope of the perpendicular bisector is -2.
Finally, we can use the point-slope form of a line to find the equation of the perpendicular bisector.
The point-slope form is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.
Using the midpoint (4, 3) as the point, the equation of the perpendicular bisector is y - 3 = -2(x - 4).