Krishna
0

Step 1: Determine the mid points on the required line.

NOTE: Note down the endpoints (x_1, y_1)and (x_2, y_2) from the given

points. And substitute the values into the midpoint formula.

[FORMULA: The midpoint formula is

M = (\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}) = (\frac{1 + 4}{2}, \frac{2 + 11}{2})

M = (\frac{5}{2}, \frac{13}{2})

where M is the midpoint of a line segment with endpoints

at (x_1, y_1) and(x_2, y_2).

Step 2: Calculate the slope of the line perpendicular to the perpendicular bisector

NOTE: m = \frac{y_2 - y_1}{x_2 - x_1}

EXAMPLE: Line AC is perpendicular to the altitude

A(1, 2), C(4, 11)

m = \frac{11 - 2}{4 - 1} = 3

Step 2: Find the slope of the perpendicular bisector

NOTE: Perpendicular gradients are connected by

EXAMPLE: Perpendicular bisector slop m(3) = -1

m = \frac{-1}{3}

Step 3: Calculate the equation of the line containing the perpendicular bisector from the midpoint and the slope.

NOTE: y - y_1 = m(x - x_1)

EXAMPLE: midpoint   (\frac{5}{2}, \frac{13}{2}) and slope   m = \frac{-1}{3}

y-\frac{13}{2}=\frac{-1}{3}(x-\frac{5}{2})

Step 4:Substitute the known values in the line equation and simplify

EXAMPLE: 3(y - \frac{13}{2}) = -1(x - \frac{5}{2})

3y - 3 * \frac{13}{2} = -x + \frac{5}{2}

6y - 39=  -2x + 5

6y + 2x = 44

3y + x = 22

Step 5: Do this for the other two medians as well.