Apply the Pythagorean theorem to find the length between (-1,6) an (5,-2) round to the nearest hundredth if necessary
To apply the Pythagorean theorem, we need to find the length of the diagonal line connecting the two given points. 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).
First, let's find the length of the horizontal side (a):
a = (5 - (-1)) = 5 + 1 = 6
Next, let's find the length of the vertical side (b):
b = (-2 - 6) = -8
Now, we can apply the Pythagorean theorem to find the length of the diagonal line (c):
c^2 = a^2 + b^2
c^2 = 6^2 + (-8)^2
c^2 = 36 + 64
c^2 = 100
c = √100
c = 10
Therefore, the length between (-1,6) and (5,-2) is 10 units.
To find the length between two points using the Pythagorean theorem, you need the coordinates of the two points. The formula for the Pythagorean theorem is:
c^2 = a^2 + b^2
where c represents the length between the two points, and a and b represent the differences in the x and y coordinates of the points.
Let's calculate the length between (-1,6) and (5,-2):
Difference in x coordinates = 5 - (-1) = 6
Difference in y coordinates = -2 - 6 = -8
Now, apply the Pythagorean theorem:
c^2 = (6^2) + (-8^2)
c^2 = 36 + 64
c^2 = 100
Therefore, c = √100 = 10
Rounding to the nearest hundredth, the length between (-1,6) and (5,-2) is 10.00.
To apply the Pythagorean theorem, you need to find the lengths of the two sides of a right triangle formed by the two given points, (-1, 6) and (5, -2).
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.
First, let's determine the length of the horizontal side, which is the difference between the x-coordinates of the two points:
Horizontal side = x2 - x1 = 5 - (-1) = 6 units
Next, let's determine the length of the vertical side, which is the difference between the y-coordinates of the two points:
Vertical side = y2 - y1 = -2 - 6 = -8 units
Note: We ignore the negative signs when finding the length of a side, as we are interested in the magnitude only.
Now, we can use the Pythagorean theorem to find the length of the hypotenuse:
Hypotenuse (c) = √((Horizontal side)² + (Vertical side)²)
Hypotenuse (c) = √(6² + (-8)²)
Hypotenuse (c) = √(36 + 64)
Hypotenuse (c) = √100
Hypotenuse (c) = 10 units (nearest hundredth)
Therefore, the length between the points (-1, 6) and (5, -2) is approximately 10 units.