MTH240 week 2
The Distance Formula
In week one, we learned a simple yet extremely useful math concept, the Distance Formula. This formula uses the Pythagorean Theorem to determine the distance between two points on the rectangular coordinate system. Variations of the Pythagorean Theorem such as the Distance Formula can be used in building things or making plans to build something.
Scenario
Suppose you are volunteering at the local community center. The community center committee is planning to install a new handicap ramp. There are several options available for surfacing the ramp but there is only a limited amount of funds for the project. To aid them in selecting an affordable surfacing option, they have asked you to determine the exact length of the purposed ramp. You know that the ramp will span 20 feet and drop 6 feet.
If you sketch a side view of the ramp on a piece of graph paper you notice that it forms a right triangle. The length of the surface of the new ramp will be equal to the long side of this right triangle. Remembering the distance formula from MTH220 class, you consider how it can be used to find the length of the ramp.
Equation and Variables The distance formula is used to find distance between two points on a rectangular coordinate system. According to our course textbook, the official formula is as follows:
d is the distance between the points. is the first point on the rectangular coordinate system. is the second point on the rectangular coordinate system (Blitzer, (2010), p. 294).
Origin of Equation
The equation is derived from the Pythagorean Theorem, . Side a and side b are the short sides of a right triangle. Side c is the long side.
In order to find the length of side a and b on a rectangular coordinate system, we must find the difference between the first point and the second point. Thus the equation takes this form:
Simplified Version of Equation We don’t need to
In week one, we learned a simple yet extremely useful math concept, the Distance Formula. This formula uses the Pythagorean Theorem to determine the distance between two points on the rectangular coordinate system. Variations of the Pythagorean Theorem such as the Distance Formula can be used in building things or making plans to build something.
Scenario
Suppose you are volunteering at the local community center. The community center committee is planning to install a new handicap ramp. There are several options available for surfacing the ramp but there is only a limited amount of funds for the project. To aid them in selecting an affordable surfacing option, they have asked you to determine the exact length of the purposed ramp. You know that the ramp will span 20 feet and drop 6 feet.
If you sketch a side view of the ramp on a piece of graph paper you notice that it forms a right triangle. The length of the surface of the new ramp will be equal to the long side of this right triangle. Remembering the distance formula from MTH220 class, you consider how it can be used to find the length of the ramp.
Equation and Variables The distance formula is used to find distance between two points on a rectangular coordinate system. According to our course textbook, the official formula is as follows:
d is the distance between the points. is the first point on the rectangular coordinate system. is the second point on the rectangular coordinate system (Blitzer, (2010), p. 294).
Origin of Equation
The equation is derived from the Pythagorean Theorem, . Side a and side b are the short sides of a right triangle. Side c is the long side.
In order to find the length of side a and b on a rectangular coordinate system, we must find the difference between the first point and the second point. Thus the equation takes this form:
Simplified Version of Equation We don’t need to