What is the distance between point A (-1,3,4) and point B at (-2,5,1)?
change in x = 1
change in y = 2
change in z = 3
d^2 = 1^2 + 2*2 + 3^2 = 1 + 4 + 9
sqrt 14
To find the distance between two points, we can use the distance formula in three-dimensional space. The distance formula is derived from the Pythagorean theorem.
The formula is as follows:
Distance = √((x2 - x1)^2 + (y2 - y1)^2 + (z2 - z1)^2)
Where:
- (x1, y1, z1) are the coordinates of point A
- (x2, y2, z2) are the coordinates of point B
In this case, the coordinates of point A are (-1, 3, 4), and the coordinates of point B are (-2, 5, 1).
Using the formula, we can calculate the distance as follows:
Distance = √((-2 - (-1))^2 + (5 - 3)^2 + (1 - 4)^2)
= √((1)^2 + (2)^2 + (-3)^2)
= √(1 + 4 + 9)
= √(14)
≈ 3.74 units
Therefore, the distance between point A (-1, 3, 4) and point B (-2, 5, 1) is approximately 3.74 units.