Help to Remember What to Learn
Pythagorean Relation
Use a2 + b2 = c2 to calculate the length of the third sided of a right triangle when the first two sides of the triangle are known.
Examples
- If a = 3 cm and b = 4 cm, calculate c.
Solution:
(3)2 + (4)2 = c2
c2 = 9 + 16
c2 = 25
c = 5 cm
- If b = 5 m and c = 13 m, calculate a.
Solution:
a2 + (5)2 = (13)2
a2 = 169 - 25
a2 = 144
a = 12 m
- If a = 7 ft and c = 25 ft, calculate b.
Solution:
(7)2 + b2 = (25)2
b2 = 625 - 49
b2 = 576
b = 24 ft
Interactive Activity
Select THE PYTHAGOREAN RELATION.
- Click on drag endpoints P and Q to change the size of the right triangle.Select the endpoint of the right angle to change the location of the triangle.
- Study the calculated distance between point P and Q provided below the graph.
- Click the applet once to activate.
Distance Formula
Knowing 2 points on the Cartesian plane, use a2 + b2 = c2 to calculate the distance between them.
Examples
- Knowing P(4, 2) and Q(8, 5), calculate the distance between them.
Solution:
Interactive Activity
Select THE DISTANCE FORMULA
- Click on drag endpoints P and Q to change the size of the right triangle.Select the endpoint of the right angle to change the location of the triangle.
- Study the calculated distance between point P and Q provided below the graph.
- Click the applet once to activate.
Midpoint Formula
Calculate the midpoint position by dividing the run and rise by two. The midpoing location will be:
Interactive Activity
- Click on drag endpoints P and Q to change the size of the right triangle.Select the endpoint of the right angle to change the location of the triangle.
- Study the calculated midpoint between point P and Q provided below the graph.
- Click the applet once to activate.