Apply the Pythagorean Theorem to find the length between (6,9) and (2,1)
To find the length between the points (6, 9) and (2, 1) using the Pythagorean theorem, we need to first calculate the difference in the x-coordinate and the difference in the y-coordinate between the two points.
Difference in x-coordinate: 2 - 6 = -4
Difference in y-coordinate: 1 - 9 = -8
Next, we use these differences to calculate the length between the two points using the Pythagorean theorem. The Pythagorean theorem states that the square of the length of the hypotenuse (c) of a right triangle is equal to the sum of the squares of the other two sides (a and b).
In this case, the lengths of the two sides (a and b) are the difference in the x-coordinate and the difference in the y-coordinate:
a = -4
b = -8
Using the Pythagorean theorem, we can calculate the length (c):
c² = a² + b²
c² = (-4)² + (-8)²
c² = 16 + 64
c² = 80
Taking the square root of both sides to find c:
c = √80
Simplifying, c is approximately equal to 8.94.
Therefore, the length between the points (6, 9) and (2, 1) is approximately 8.94 units.