Apply the Pythagorean Theorem to find the length between (2, 5)

Question

(
2
,

5
)
and (7, 3)
(
7
,

3
)
. Round your answer to the nearest hundredth, if necessary.(1 point)
Responses

2.65
2.65

5.39
5.39

29
29

4.58

Answer 1

To find the distance between the points \((2, 5)\) and \((7, 3)\) using the Pythagorean Theorem, you can use the distance formula:

\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

Where \((x_1, y_1)\) and \((x_2, y_2)\) are the coordinates of the two points.

In this case:

• \((x_1, y_1) = (2, 5)\)
• \((x_2, y_2) = (7, 3)\)

Now substitute the values into the formula:

\[ d = \sqrt{(7 - 2)^2 + (3 - 5)^2} \] \[ d = \sqrt{(5)^2 + (-2)^2} \] \[ d = \sqrt{25 + 4} \] \[ d = \sqrt{29} \]

Now calculate \(\sqrt{29}\):

\[ \sqrt{29} \approx 5.385 \]

Rounding to the nearest hundredth, the distance is approximately \(5.39\).

Thus, the answer is:

5.39

Answer 2

Apply the Pythagorean Theorem to find the length between (−1, 6)
(
−
1
,

6
)
and (5, −2)
(
5
,

−
2
)
. Round your answer to the nearest hundredth, if necessary.(1 point)
Responses

100
100

14
14

10
10

9.22

Answer 3

To find the distance between the points \((-1, 6)\) and \((5, -2)\) using the Pythagorean Theorem, we will use the distance formula:

\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

Where:

• \((x_1, y_1) = (-1, 6)\)
• \((x_2, y_2) = (5, -2)\)

Substituting the values into the formula, we get:

\[ d = \sqrt{(5 - (-1))^2 + (-2 - 6)^2} \] \[ d = \sqrt{(5 + 1)^2 + (-8)^2} \] \[ d = \sqrt{(6)^2 + (-8)^2} \] \[ d = \sqrt{36 + 64} \] \[ d = \sqrt{100} \]

Calculating \(\sqrt{100}\):

\[ d = 10 \]

Thus, the distance between the points \((-1, 6)\) and \((5, -2)\) is \(10\).

Therefore, the answer is:

10

Answer 4

Apply the Pythagorean Theorem to find the length between the two points. Round your answer to the nearest hundredth, if necessary.

(1 point)
Responses

5.57
5.57

9
9

41
41

6:40

Answer 5

It seems that you haven't provided the specific coordinates of the two points for which you want to determine the distance. Please provide the coordinates, and I can calculate the distance using the Pythagorean Theorem (distance formula) and round it to the nearest hundredth if necessary.