Question

​ If the endpoints of line AB are A(7,3) and B(5,-1), what is the length of line AB?

Answer 1

The length of line AB with endpoints A(7,3) and B(5,-1) is calculated using the distance formula, resulting in a length of 2√5 units.

Step-by-step explanation:

To find the length of line AB with endpoints A(7,3) and B(5,-1), you can use the distance formula derived from the Pythagorean theorem. The distance formula is d = √((x2 - x1)^2 + (y2 - y1)^2), where (x1, y1) and (x2, y2) are the coordinates of the two points.

For the given points A(7,3) and B(5,-1), the length of line AB is calculated as follows:

1. Subtract the x-coordinates of A and B: 5 - 7 = -2.
2. Subtract the y-coordinates of A and B: 3 - (-1) = 4.
3. Square each difference: (-2)^2 = 4 and 4^2 = 16.
4. Add the squares: 4 + 16 = 20.
5. Take the square root of the sum: √20.
6. Simplify the square root if possible: √20 = 2√5, which is the length of line AB.

Therefore, the length of line AB is 2√5 units.