0
The Pythagorean theorem defines Euclidean distance between two points in space.
If the coordinates of A are (xa, ya, za) and those of B are (xb, yb, zb) then, using the Pythagoras theorem in 3-dimensions,
|AB| = sqrt[(xa - xb)2 + (ya - yb)2 + (za - zb)2]
However, Euclidean distance is not the only distance metric. A simple example of a non-Euclidean metric is the metric variously known as the Taxicab, Manhattan or Minkowski metric. This is based on a grid of mutually perpendicular lines and the distance between two points A = (p, q) and B = (r, s) is (r-p) + (s-q). To go from A to B on the grid of streets and avenues in [downtown] Manhattan, the cab has to go travel (r-p) units in one direction and (s-q) in an orthogonal direction.
There are many other possible metrics. So, the Pythagorean theorem is only one of many possible formulae for distance.
What else can I help you with?
Is The Distance Formula is derived from the Pythagorean Theorem?
No.
What formula is used to find the length between two points in a coordinate plane?
It is the Pythagorean distance formmula.If P = (x1, y1) and Q = (x2, y2) thenDistance between P and Q = sqrt[(x1 - x2)2 + (y1 - y2)2]It is the Pythagorean distance formmula.If P = (x1, y1) and Q = (x2, y2) thenDistance between P and Q = sqrt[(x1 - x2)2 + (y1 - y2)2]It is the Pythagorean distance formmula.If P = (x1, y1) and Q = (x2, y2) thenDistance between P and Q = sqrt[(x1 - x2)2 + (y1 - y2)2]It is the Pythagorean distance formmula.If P = (x1, y1) and Q = (x2, y2) thenDistance between P and Q = sqrt[(x1 - x2)2 + (y1 - y2)2]
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.
To find the distance between any two points in the planes do you distance formula?
Yes
How is the distance formula related to the pythagorean theorem?
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.
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.
Is this true or false the distance formula is equivalent to the Pythagorean theorm if your trying to find the distance between a point in the plane and the origin?
True. The distance formula, which is derived from the Pythagorean theorem, calculates the distance between two points in a plane. When finding the distance between a point ((x, y)) and the origin ((0, 0)), the formula simplifies to (d = \sqrt{x^2 + y^2}), which directly corresponds to the Pythagorean theorem. Thus, in this specific case, the distance formula is indeed equivalent to the Pythagorean theorem.
The Pythagorean Theorem is similar to?
the slope formula and the distance formula.
Is The Distance Formula is derived from the Pythagorean Theorem?
No.
The pythagorean theorem can be developed from what?
distance formula!
Given the coordinates of two points in the plane you can use either the distance formula or the Pythagorean theorem to find the distance between them.?
Verdadero
Can the distance formula can be derived from the Pythagorean theorem?
Yes, the formula for the Euclidean distance. But not necessarily other distance metrics.
Is The pythagorean theroem derived from the distance formula?
the answer is false
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.
Is it true that Given the coordinates of two points in the plane you can use either the distance formula or the Pythagorean theorem to find the distance between them?
Yes it is true
What is better to use The Distance Formula or The Pythagorean Theorem?
false
Is the distance formula derived from Pythagorean theorem?
Yes, the distance formula for a line segment was derived from Pythagoras' theorem.
