Answer:
3y = x + 7.
Explanation:
The locus will be a line perpendicular to and passing through the centre of the line joining the 2 points.
The midpoint of (4, 2) and (3, 5) is
[(4+3)/2, (2+5 / 2)=
= (3.5 , 3.5).
The slope of the line joining the 2 points is
(5-2)(3-4) = -3.
So, the slope of the perpendicular line = -1 / -3 = 1/3.
Now we find the required locus by using the point-slope form of the straight line and the above results:
y - y1 = m(x - x1)
Here m = 1/3, x1 = 3.3 and y1 = 3.5 so:
y - 3.5 = 1/3(x - 3.5)
y = 1/3x - 3.5/3 + 3.5
Multiplying through by 3:
3y = x - 3.5 + 10.5
3y = x + 7.