Question

distance AB between the points A (2,3,4) and B (-5,6,7) is given by :​

Answer 1

Step-by-step explanation:

Learn how to find the distance between two points by using the distance formula, which is an application of the Pythagorean theorem. We can rewrite the Pythagorean theorem as d=√((x_2-x_1)²+(y_2-y_1)²) to find the distance between any two points. Created by Sal Khan and CK-12 Foundation.

Answer 2

The distance AB between the points A (2,3,4) and B (-5,6,7) is √67 unit

Given :

The points A (2,3,4) and B (-5,6,7)

To find :

The distance AB between the points A (2,3,4) and B (-5,6,7)

Formula :

For the given two points ( x₁ , y₁, z₁ ) & (x₂ , y₂, z₂ ) the distance between the points

$= \sf{ \sqrt{ {(x_2 -x_1 )}^{2} + {(y_2 -y_1 )}^{2}+ {(z_2 - z_1 )}^{2} } }$

Solution :

Step 1 of 2 :

Write down the given points

Here the given points are A (2,3,4) and B (-5,6,7)

Step 2 of 2 :

Find the distance AB between the points

The distance AB between the points

$\displaystyle \sf{ = \sqrt{ {(2 + 5)}^{2} + {(3 - 6)}^{2} + {(4 - 7)}^{2} } \: \: \: unit }$

$\displaystyle \sf{ = \sqrt{ {(7)}^{2} + {( - 3)}^{2} + {( - 3)}^{2} } \: \: \: unit }$

$\displaystyle \sf{ = \sqrt{ 49 + 9 + 9 } \: \: \: unit }$

$\displaystyle \sf{ = \sqrt{ 67 } \: \: \: unit }$

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