Category Archives: Trigsted Chapter 2

Finding the Midpoint

The Midpoint Formula

Suppose A is ( x_1,   y_1) and B is ( x_2,    y_2)

The midpoint of the line segment joining points A and B is given by the following formula.

( {x_1+x_2}/2,   {y_1+y_2}/2)

Example: Find the midpoint of a line segment joining points A and B.

Point A is ( 4, -2) and point B is ( -8, 3)

The x coordinate of the midpoint can be found by averaging the x-values of point A and B.  The y-coordinate of the midpoint can be found by averaging the y-values of point A and B.

( {4+(-8)}/2,   {-2+3}/2)

( {-4}/2,   {1}/2)

( -2,   {1}/2)

Finding the equation of a line perpendicular to another line

Example: Find the equation of a line perpendicular to another line and passing through a specific point. (The other line in slope intercept form)

Example: Find the equation of a line perpendicular to another line and passing through a specific point. (The other line in slope standard form)

Example: Find the equation of a line perpendicular to the x-axis.

Example: Find the equation of a line perpendicular to the x-axis and perpendicular to the y-axis.

 

Finding the Equation of a Line parallel to another line

Example: Find the equation of the line parallel to another line and passing through a specific point. (parallel equation in slope intercept form)

Example: Find the equation of the line parallel to another line and passing though a specific point. (parallel line in standard form)

Example: Find the equation of the line parallel to the x-axis or y-axis and passing through a specific point.

Example: What is an equation parallel to the y-axis?

Example: What is an equation parallel to the x-axis?