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Take any two points in the plane. Let' s call them P1 and P2 and they have coordinates
(x1,y1) and (x2, y2) respectively.
Now if we want to find the distance between them, we use
the distance formula. But what this formula is really doing is using the pythagorean theorem. Here is why.
You want to find the distance from P1 to P2. Construct a line from x1 to x2 and y1 to y2.
The straight line between P1 and P2 is the hypotenuse of the right triangle you just created. Now, Pythagoras says, that the hypotenuse squared is equal to the sum of the squares of the side. But we need the the length of those sides. The horizontal one is (x2-x1) and the vertical one is (y2-y1). So if we look at (x2-x1)2+(y2-y1)2 this is equal to hypotenuse
of the triangle squared. But the hypotenuse is the distance from P1 to P2.
So if we take the square root of that hypotenuse, we must also take square root
(x2-x1)2+(y2-y1)2 AND this is exactly what the distance formula shows.
It would help to draw a picture to see this.
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Is The Distance Formula is derived from the Pythagorean Theorem?
No.
Converse of Pythagorean Theorem?
The Pythagorean Theorem allows the mathematician to determine the value of the hypotenuse. The converse of the Pythagorean Theorem manipulates the formula so that the mathematician can use the values to determine that if the triangle is a right triangle.
Which formula can be derived by using the Pythagorean theorem in the coordinate plane?
The Pythagorean theorem, which is the square root of the sum of the squares of two sides of a right triangle is equal to the hypotenuse, can be used to find the distance between two points. This means that it can also be used to find the equation of a line.
What is the difference between the pythagorean theorem and the converse of the pythagorean theorem?
The Pythagorean Theorem states that in a right triangle with legs a and b and hypotenuse c, a2 + b2 = c2. The converse of the Pythagorean theorem states that, if in a triangle with sides a, b, c, a2 + b2 = c2 then the triangle is right and the angle opposite side c is a right angle.
How do you find the perimeter of a parallelogram using Pythagorean theorem?
you can't, because the Pythagorean theorem is for right triangles and the triangles formed by the diagonal of a parallelogram are not right triangles.
What is the difference in the distance formula and the Pythagorean theorem?
The difference in the distance formula and the pythagorean theorem is that the distance formula finds the distance between two points while the pythagorean theorem usually finds the hypotenuse of a right triangle.
What is better the pythagorean therom or the disance formula?
Better for what??? Actually, both are closely related. The distance formula is derived from the Pythagorean theorem.
The pythagorean theorem can be developed from what?
distance formula!
Is The Distance Formula is derived from the Pythagorean Theorem?
No.
The Pythagorean Theorem is similar to?
the slope formula and the distance formula.
Is the distance formula derived from Pythagorean theorem?
Yes, the distance formula for a line segment was derived from Pythagoras' theorem.
What is better to use The Distance Formula or The Pythagorean Theorem?
false
Is Pythagorean theorem is derived from the distance formula?
Yes, the distance formula for a line segment was derived from Pythagoras' theorem.
Can the distance formula can be derived from the Pythagorean theorem?
Yes, the formula for the Euclidean distance. But not necessarily other distance metrics.
The Pythagorean Theorem is always better to use than the Distance Formula?
False.
The distance formula is derived from the Pythagorean theorem. true or false?
True
How might the Pythagorean theorem and distance formula be used in everyday life?
Carpentry
