Find the equation of a straight line which is equidistant from the points A(2,3)andB(6,1)
To find the equation of a straight line equidistant from two points A(2,3) and B(6,1), we can start by finding the midpoint of AB.
The midpoint formula is given by: [(x1 + x2)/2, (y1 + y2)/2]
Using this formula, the midpoint of AB can be calculated as:
[(2 + 6)/2, (3 + 1)/2] = (4, 2)
Now, let's find the slope of line AB using the formula: m = (y2 - y1)/(x2 - x1)
m = (1 - 3)/(6 - 2) = -2/4 = -1/2
Since the line we're looking for is equidistant from A and B, it means the perpendicular bisector of AB passes through the midpoint (4, 2).
The slope of a line perpendicular to AB is the negative reciprocal of -1/2, which is 2.
Now we can use the point-slope form of a line to find the equation with the midpoint (4, 2) and slope 2:
y - y1 = m(x - x1)
y - 2 = 2(x - 4)
Expanding this equation, we get:
y - 2 = 2x - 8
Simplifying, we get:
y = 2x - 6
Therefore, the equation of the straight line equidistant from points A(2,3) and B(6,1) is y = 2x - 6.