The equation of perpendicular bisector of line segment joining (4, 2) and (–2, 0) is :-x + y = 23x + y = 42x – y = 1None of these

The first step is to find the midpoint of the line segment joining the points (4, 2) and (-2, 0).

The formula for the midpoint is ((x1 + x2)/2, (y1 + y2)/2).

Substituting the given points into the formula, we get:

Midpoint = ((4 + -2)/2, (2 + 0)/2) = (1, 1)

Next, we need to find the slope of the line segment. The formula for the slope is (y2 - y1) / (x2 - x1).

Substituting the given points into the formula, we get:

Slope = (0 - 2) / (-2 - 4) = 2/6 = 1/3

The slope of the perpendicular bisector is the negative reciprocal of the slope of the line segment. So, the slope of the perpendicular bisector is -3.

Finally, we can find the equation of the perpendicular bisector using the point-slope form of a line, which is y - y1 = m(x - x1).

Substituting the midpoint (1, 1) and the slope -3, we get:

y - 1 = -3(x - 1)

Solving for y, we get:

y = -3x + 4

So, the equation of the perpendicular bisector of the line segment joining (4, 2) and (-2, 0) is y = -3x + 4.

Therefore, the correct answer is "None of these".