Answer:
AB is y = -3x + 7.
Step-by-step explanation:
To find the equation of the perpendicular bisector of line AB with points A(-2,3) and B(4,5), we first need to find the midpoint of AB and then determine the slope of the line AB.
The midpoint of AB is given by the formula:
((x1 + x2)/2, (y1 + y2)/2)
So, the midpoint M of AB is:
((-2 + 4)/2, (3 + 5)/2)
= (1, 4)
The slope of line AB is given by the formula:
m = (y2 - y1) / (x2 - x1)
So, the slope of AB is:
(5 - 3) / (4 - (-2))
= 2 / 6
= 1/3
The negative reciprocal of the slope of AB is the slope of the perpendicular bisector. So the slope of the perpendicular bisector is -3.
Now that we have the midpoint and the slope of the perpendicular bisector, we can use the point-slope form of a line to find its equation. The point-slope form is:
y - y1 = m(x - x1)
Using the midpoint M(1, 4) and the slope -3, the equation of the perpendicular bisector is:
y - 4 = -3(x - 1)
y - 4 = -3x + 3
y = -3x + 7
Therefore, the equation of the perpendicular bisector of line AB is y = -3x + 7.