Apply the Pythagorean Theorem to find the length between (2, 5) and (7, 3) . Round your answer to the nearest hundredth, if necessary.(1 point)
a.5.38
b.29
c.2.65
d.4.58
The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In this case, the points (2, 5) and (7, 3) form the two sides of a right triangle, and we want to find the length of the hypotenuse.
First, we calculate the length of the horizontal side of the triangle:
7 - 2 = 5
Next, we calculate the length of the vertical side of the triangle:
3 - 5 = -2
Since we need to find the length, we take the absolute value of -2:
|-2| = 2
Now, we use the Pythagorean Theorem to find the length of the hypotenuse:
hypotenuse^2 = (horizontal side)^2 + (vertical side)^2
hypotenuse^2 = 5^2 + 2^2
hypotenuse^2 = 25 + 4
hypotenuse^2 = 29
To find the length of the hypotenuse, we take the square root of both sides:
hypotenuse = √29 ≈ 5.385
Rounded to the nearest hundredth, the length between (2, 5) and (7, 3) is approximately 5.38.
The answer is a. 5.38.
wrong
My apologies for the mistake.
To find the length between the points (2, 5) and (7, 3), we can use the distance formula, which is a direct application of the Pythagorean theorem.
The distance formula is given by:
d = √[(x2 - x1)^2 + (y2 - y1)^2]
Using the coordinates (2, 5) and (7, 3), we can plug them into the formula:
d = √[(7 - 2)^2 + (3 - 5)^2]
= √[(5)^2 + (-2)^2]
= √[25 + 4]
= √29
Rounded to the nearest hundredth, the length between (2, 5) and (7, 3) is approximately 5.39.
The correct answer is not listed among the options provided.
To apply the Pythagorean Theorem to find the length between two points, you need to follow these steps:
1. Identify the coordinates of the two points. In this case, the coordinates are (2, 5) and (7, 3).
2. Use the formula: d = √((x2 - x1)^2 + (y2 - y1)^2), where (x1, y1) and (x2, y2) are the coordinates of the two points.
3. Substitute the values into the formula: d = √((7 - 2)^2 + (3 - 5)^2).
Simplifying the equation:
d = √(5^2 + (-2)^2)
d = √(25 + 4)
d = √29
4. Round the answer to the nearest hundredth, if necessary. In this case, it is necessary to round the answer.
5. The final answer is approximately 5.38.
Therefore, the correct answer is a. 5.38.