Processes for Median, Altitudes, Perpendicular Bisectors and POIs

Question 1

Medians

Answer 1

1. Calculate midpoint of the relevant line using (x1+x2/2, y1+y2/2)
2. Calculate gradient of the line between midpoint and opposite corner using
   y2-y1/x2-x1
3. Find the equation using this gradient and either of the points (whichever is easier)

Question 2

Altitude

Answer 2

1. Calculate the gradient of the side which is perpendicular to the altitude using
   m=y2-y1/x2-x1
2. Calculate the gradient of the altitude using m x m perpendicular = -1 (flip the sign and turn the number inside out ( 5 would go to
   - 1/5 for example)
3. Find the equation using this gradient and the point the altitude passes through using the equation y-b = m(x-a)

Question 3

Perpendicular lines

Answer 3

1. Calculate the midpoint of the line segment being bisected using M = (x1+x1/2, y1+y2/2)
2. Calculate the gradient of the line used used in step 1 using the equation m=y2-y1/x2-x1.
3. Using this gradient use the equation m x m perpendicular = -1 (flip the sign and turn the number inside out, -1/3 becomes 3)
4. Find the equation of the perpendicular bisector using the point from step 1 and gradient from step 3 inserting into the equation y-b = m(x-a)

Question 4

POIs

Answer 4

After finding two of these aforementioned lines put them into a simultaneous equation or use y=y and consequently finding y and x.

Question 5

What is a perpendicular bisector.

Answer 5

A line that cuts another line directly in half and at right angles to said line.

Question 6

What is a median?

Answer 6

A line that goes from the middle of one line to the corner of another in a triangle.

Question 7

What is an altitude ?

Answer 7

A line that goes from the corner of a triangle to cut another line at right angles within the triangle.