Apply the Pythagorean Theorem to find the length Between (2,5) and (7,3). Round your answers to the nearest hundredth if necessary.
To apply the Pythagorean Theorem to find the length between the points (2,5) and (7,3), we need to find the distance between the x-coordinates and the distance between the y-coordinates.
The distance between the x-coordinates is calculated by subtracting the x-coordinate of one point from the x-coordinate of the other point:
7 - 2 = 5
Similarly, the distance between the y-coordinates is calculated by subtracting the y-coordinate of one point from the y-coordinate of the other point:
3 - 5 = -2
Now, we can use these distances to find the length between the two points by applying the Pythagorean Theorem:
Length = √((distance between x-coordinates)^2 + (distance between y-coordinates)^2)
= √(5^2 + (-2)^2)
= √(25 + 4)
= √29
Since we are asked to round the answer to the nearest hundredth, the length between the given points is approximately 5.39.
To apply the Pythagorean Theorem to find the length between two points in a coordinate plane, we first need to identify the coordinates of the two points.
In this case, the given points are (2,5) and (7,3).
Using the Pythagorean Theorem:
1. Find the difference in the x-coordinates:
(7 - 2) = 5.
2. Find the difference in the y-coordinates:
(3 - 5) = -2.
3. Square the differences in the x and y-coordinates:
(5^2) = 25 and (-2^2) = 4.
4. Add the squared differences together:
25 + 4 = 29.
5. Take the square root of the sum to find the length:
√(29) ≈ 5.39.
Therefore, the length between the points (2,5) and (7,3) is approximately 5.39 (rounded to the nearest hundredth).
To apply the Pythagorean Theorem, you need to find the length of the hypotenuse of a right triangle, given the lengths of its legs. In this case, the legs of the right triangle represent the horizontal and vertical distances between the two given points.
First, find the horizontal distance (x) between the two points:
x = 7 - 2 = 5
Then, find the vertical distance (y) between the two points:
y = 3 - 5 = -2
Note that since distance is always positive, we take the absolute value of the vertical distance.
Next, use the Pythagorean Theorem formula:
c^2 = a^2 + b^2
where c is the length of the hypotenuse (which we need to find), and a and b are the lengths of the legs.
Substituting the values we found:
c^2 = 5^2 + (-2)^2
c^2 = 25 + 4
c^2 = 29
To find the length of the hypotenuse, take the square root of both sides:
c = √29
Rounding to the nearest hundredth, c ≈ 5.39.
Therefore, the length between (2,5) and (7,3) is approximately 5.39 units.