Find the distance between the following points using the Pythagorean theorem: (11, 9) and (-3, 11)
20 units
2002 units
200 units
200−−−√ units
To find the distance between two points using the Pythagorean theorem, we need to find the length of the hypotenuse of a right triangle formed by the two points.
Let's label the first point (x1, y1) = (11, 9) and the second point (x2, y2) = (-3, 11).
The distance between the two points is given by the formula:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Substituting the values:
d = √((-3 - 11)^2 + (11 - 9)^2)
Simplifying:
d = √((-14)^2 + (2)^2)
d = √(196 + 4)
d = √200
The distance between the two points is 20 units.
A disk is in the form of square and measures 5.25 inches on each side. Find the diagonal length of the disk.
7.4 inches
6.5 inches
5.5 inches
4.5 inches
To find the diagonal length of a square, we can use the Pythagorean theorem.
The diagonal (d) of a square with sides of length (s) can be found using the formula:
d = √(s^2 + s^2)
Given that the side length of the square disk is 5.25 inches, we can substitute this value into the formula.
d = √(5.25^2 + 5.25^2)
d = √(27.56 + 27.56)
d = √55.12
d ≈ 7.4 inches
Therefore, the diagonal length of the disk is approximately 7.4 inches.
Find the distance between the following points using the Pythagorean theorem: (-3, -7), (2, 5)
13 units
17 units
26 units
169 units
To find the distance between two points using the Pythagorean theorem, we need to find the length of the hypotenuse of a right triangle formed by the two points.
Let's label the first point (x1, y1) = (-3, -7) and the second point (x2, y2) = (2, 5).
The distance between the two points is given by the formula:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Substituting the values:
d = √((2 - (-3))^2 + (5 - (-7))^2)
Simplifying:
d = √((2 + 3)^2 + (5 + 7)^2)
d = √((5)^2 + (12)^2)
d = √(25 + 144)
d = √169
The distance between the two points is 13 units.
Find the distance between the following points using the Pythagorean theorem: (5, 10) and (10, 12)
29 units
15.13 units
29−−√ units
22.56 units
To find the distance between two points using the Pythagorean theorem, we need to find the length of the hypotenuse of a right triangle formed by the two points.
Let's label the first point (x1, y1) = (5, 10) and the second point (x2, y2) = (10, 12).
The distance between the two points is given by the formula:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Substituting the values:
d = √((10 - 5)^2 + (12 - 10)^2)
Simplifying:
d = √((5)^2 + (2)^2)
d = √(25 + 4)
d = √29
The distance between the two points is √29 units, which is equivalent to approximately 5.39 units.