Use the Pythagorean Theorem to find the distance between (2, 5) and (7,3)
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
To find the distance between points (2, 5) and (7, 3), we can consider these points as the vertices of a right triangle, with the distance between them as the hypotenuse. We can calculate the lengths of the other two sides and then apply the Pythagorean theorem.
The vertical side is the difference in the y-coordinates, so it is 5 - 3 = 2.
The horizontal side is the difference in the x-coordinates, so it is 7 - 2 = 5.
Applying the Pythagorean theorem:
Distance^2 = vertical side^2 + horizontal side^2
Distance^2 = 2^2 + 5^2
Distance^2 = 4 + 25
Distance^2 = 29
Taking the square root of both sides to find the distance:
Distance = √(29)
Thus, the distance between (2, 5) and (7, 3) is approximately 5.39 units.
whats the square root of 29
The square root of 29 is approximately 5.39.
use the pythagorean theorem to find the distance between (-1, 6) and (5, -2)
To find the distance between (-1, 6) and (5, -2), we need to calculate the length of the hypotenuse of the right triangle formed by these points.
The vertical side of the triangle is the difference in y-coordinates: 6 - (-2) = 8.
The horizontal side of the triangle is the difference in x-coordinates: 5 - (-1) = 6.
Applying the Pythagorean theorem:
Distance^2 = vertical side^2 + horizontal side^2
Distance^2 = 8^2 + 6^2
Distance^2 = 64 + 36
Distance^2 = 100
Taking the square root of both sides to find the distance:
Distance = √(100)
Thus, the distance between (-1, 6) and (5, -2) is 10 units.