Vanessa Otero
Geometry
How a distance formula is the same thing as Pythagorean theorem.
The distance formula and Pythagorean theorem are the same in the following ways. Pythagorean theorem shows that on a right triangle the sides connected to that angle both squared will equal the length of the third side of the triangle. The distance formula shows the distance of a segment from one point to another on a coordinate graph. After the first step in distance formula, you end up with Pythagorean theorem and solve for distance. For example, the distance formula is (x2 – x1)+(y2 – y1) once you solve the first step with your coordinates you end up with x2 + y2 which ends up being Pythagorean theorem.
In Pythagorean theorem you have two lengths and have to find the third length, which is a hypotenuse. The hypotenuses is the only longest side of a right triangle and just like with any equation if you have two parts of the equation you can solve. When you do the distance formula you have to plug in the coordinates of any point in a segment and subtract. Then the formula turns into the same thing as Pythagorean theorem, because all you’re doing is taking the coordinates you have and solving.
In conclusion, the distance formula and Pythagorean theorem are proven that they are similar to each other because the formula turns into Pythagorean theorem. Once you get more advanced in math, you start to really get used to the distance formula and be able to go straight to Pythagorean theorem.
Geometry
How a distance formula is the same thing as Pythagorean theorem.
The distance formula and Pythagorean theorem are the same in the following ways. Pythagorean theorem shows that on a right triangle the sides connected to that angle both squared will equal the length of the third side of the triangle. The distance formula shows the distance of a segment from one point to another on a coordinate graph. After the first step in distance formula, you end up with Pythagorean theorem and solve for distance. For example, the distance formula is (x2 – x1)+(y2 – y1) once you solve the first step with your coordinates you end up with x2 + y2 which ends up being Pythagorean theorem.
In Pythagorean theorem you have two lengths and have to find the third length, which is a hypotenuse. The hypotenuses is the only longest side of a right triangle and just like with any equation if you have two parts of the equation you can solve. When you do the distance formula you have to plug in the coordinates of any point in a segment and subtract. Then the formula turns into the same thing as Pythagorean theorem, because all you’re doing is taking the coordinates you have and solving.
In conclusion, the distance formula and Pythagorean theorem are proven that they are similar to each other because the formula turns into Pythagorean theorem. Once you get more advanced in math, you start to really get used to the distance formula and be able to go straight to Pythagorean theorem.