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Use the image to answer the question.

Apply the Pythagorean Theorem to find the length of the diagonal of the square. Round your answer to the nearest hundredth, if necessary.

(1 point)
Responses

2.83
2.83

4
4

8
8

4.24
4.24

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

5
)
and (7, 3)
(
7
,

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

4.58
4.58

2.65
2.65

29
29

5.39

3. 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

9.22
9.22

100
100

10
10

14

4. Use the image to answer the question.A graph shows four quadrants with the x-axis and y-axis both ranging from negative 5 to positive 5 in increments of 1. Unlabeled data points marked are at left parenthesis negative 2 comma negative 1 right parenthesis, and at left parenthesis 2 comma 4 right parenthesis. A straight line joins the two lines with a positive slope.Apply the Pythagorean Theorem to find the length between the two points. Round your answer to the nearest hundredth, if necessary.(1 point)Responses
6:40
5.57
41
9

5. Use the image to answer the question.A graph shows four quadrants with the x-axis and y-axis both ranging from negative 5 to positive 5 in increments of 1. Data points marked are point A at left parenthesis 2 comma negative 3 right parenthesis, and point B at left parenthesis 5 comma 5 right parenthesis. Apply the Pythagorean Theorem to find the length between the two points. Round your answer to the nearest hundredth, if necessary.(1 point)Responses
11
7.62
73
8.54

7 answers

Let’s solve each problem step by step.

  1. Finding the length of the diagonal of a square: If the side of the square is \(s\), then by the Pythagorean theorem, the diagonal \(d\) can be calculated as: \[ d = \sqrt{s^2 + s^2} = \sqrt{2s^2} = s\sqrt{2} \] Without specific information given about \(s\), I cannot provide a numeric answer.

  2. Finding the length between the points (2, 5) and (7, 3): Use the distance formula: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] where \((x_1, y_1) = (2, 5)\) and \((x_2, y_2) = (7, 3)\). \[ d = \sqrt{(7 - 2)^2 + (3 - 5)^2} = \sqrt{5^2 + (-2)^2} = \sqrt{25 + 4} = \sqrt{29} \approx 5.39 \] So the answer is 5.39.

  3. Finding the length between the points (-1, 6) and (5, -2): Using the distance formula again: \[ d = \sqrt{(5 - (-1))^2 + (-2 - 6)^2} = \sqrt{(5 + 1)^2 + (-8)^2} = \sqrt{6^2 + (-8)^2} = \sqrt{36 + 64} = \sqrt{100} = 10 \] So the answer is 10.

  4. Finding the length between the points (-2, -1) and (2, 4): Again, use the distance formula: \[ d = \sqrt{(2 - (-2))^2 + (4 - (-1))^2} = \sqrt{(2 + 2)^2 + (4 + 1)^2} = \sqrt{4^2 + 5^2} = \sqrt{16 + 25} = \sqrt{41} \approx 6.40 \] So the answer is 6.40.

  5. Finding the length between the points (2, -3) and (5, 5): Finally, apply the distance formula: \[ d = \sqrt{(5 - 2)^2 + (5 - (-3))^2} = \sqrt{(3)^2 + (5 + 3)^2} = \sqrt{3^2 + 8^2} = \sqrt{9 + 64} = \sqrt{73} \approx 8.54 \] So the answer is 8.54.

In summary:

  1. Diagonal of the square: Not enough information provided.
  2. Distance between (2, 5) and (7, 3): 5.39
  3. Distance between (-1, 6) and (5, -2): 10
  4. Distance between (-2, -1) and (2, 4): 6.40
  5. Distance between (2, -3) and (5, 5): 8.54
Use the image to answer the question.A graph shows quadrant 1 with the x-axis and y-axis ranging from 0 to positive 5. Data points marked are point A at left parenthesis 1 comma 2 right parenthesis, point B at left parenthesis 3 comma 2 right parenthesis, point C at left parenthesis 3 comma 4 right parenthesis, and point D at left parenthesis 1 comma 4 right parenthesis. A line joins points A to B, B to C, C to D, and D to A, forming a rectangle.Apply the Pythagorean Theorem to find the length of the diagonal of the square. Round your answer to the nearest hundredth, if necessary.(1 point)Responses2.832.8344884.244.24Skip to navigation
Your image shows a square on a coordinate plane with points labeled A, B, C, and D. Here are the details:

Point A: (1, 2)

Point B: (3, 2)

Point C: (3, 4)

Point D: (1, 4)

The square is outlined in orange with black dots marking each vertex, and the x-axis and y-axis range from 0 to 5.

To find the length of the diagonal of the rectangle formed by points A, B, C, and D, we first need to determine the length of one side of the rectangle.

The points are:

  • Point A: \( (1, 2) \)
  • Point B: \( (3, 2) \)
  • Point C: \( (3, 4) \)
  • Point D: \( (1, 4) \)

Step 1: Determine the Lengths of the Sides

  • The length from A to B (horizontal side): \[ \text{Length} = x_B - x_A = 3 - 1 = 2 \]

  • The length from B to C (vertical side): \[ \text{Length} = y_C - y_B = 4 - 2 = 2 \]

Step 2: Calculate the Length of the Diagonal

The diagonal \(d\) of the rectangle can be calculated using the Pythagorean theorem: \[ d = \sqrt{\text{(length of side 1)}^2 + \text{(length of side 2)}^2} \] In this case: \[ d = \sqrt{(2)^2 + (2)^2} = \sqrt{4 + 4} = \sqrt{8} = 2\sqrt{2} \]

Step 3: Approximate \(2\sqrt{2}\)

Calculating \(2\sqrt{2}\): \[ 2\sqrt{2} \approx 2 \times 1.414 = 2.828 \]

Step 4: Round to the Nearest Hundredth

Rounding \(2.828\) to the nearest hundredth gives us: \[ 2.83 \]

Final Answer

So, the length of the diagonal of the rectangle is 2.83.

Use the image to answer the question.A graph shows quadrant 1 with the x-axis and y-axis ranging from 0 to positive 5. Data points marked are point A at left parenthesis 1 comma 2 right parenthesis, point B at left parenthesis 3 comma 2 right parenthesis, point C at left parenthesis 3 comma 4 right parenthesis, and point D at left parenthesis 1 comma 4 right parenthesis. A line joins points A to B, B to C, C to D, and D to A, forming a rectangle.Apply the Pythagorean Theorem to find the length of the diagonal of the square. Round your answer to the nearest hundredth, if necessary.(1 point)Responses
8
4.24
2.83
4

2. 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)
Responses

2.65

5.39

29

4.58

3. 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.

4. se the image to answer the question.A graph shows four quadrants with the x-axis and y-axis both ranging from negative 5 to positive 5 in increments of 1. Unlabeled data points marked are at left parenthesis negative 2 comma negative 1 right parenthesis, and at left parenthesis 2 comma 4 right parenthesis. A straight line joins the two lines with a positive slope.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
9
41
6.40

5. Use the image to answer the question.A graph shows four quadrants with the x-axis and y-axis both ranging from negative 5 to positive 5 in increments of 1. Data points marked are point A at left parenthesis 2 comma negative 3 right parenthesis, and point B at left parenthesis 5 comma 5 right parenthesis. Apply the Pythagorean Theorem to find the length between the two points. Round your answer to the nearest hundredth, if necessary.(1 point)Responses
11
7.62
73
8.54

Let’s solve each problem step-by-step using the information provided.

1. Diagonal of the Rectangle (Points A, B, C, D)

Using the points given:

  • Point A: \( (1, 2) \)
  • Point B: \( (3, 2) \)
  • Point C: \( (3, 4) \)
  • Point D: \( (1, 4) \)

The rectangle has its width and height as follows:

  • Width (AB): \(3 - 1 = 2\)
  • Height (BC): \(4 - 2 = 2\)

To find the diagonal \(d\) using the Pythagorean theorem: \[ d = \sqrt{(\text{width})^2 + (\text{height})^2} = \sqrt{(2)^2 + (2)^2} = \sqrt{4 + 4} = \sqrt{8} = 2\sqrt{2} \approx 2.83 \]

Answer: 2.83

2. Length Between Points (2, 5) and (7, 3)

Using the distance formula: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] For points \( (2, 5) \) and \( (7, 3) \): \[ d = \sqrt{(7 - 2)^2 + (3 - 5)^2} = \sqrt{5^2 + (-2)^2} = \sqrt{25 + 4} = \sqrt{29} \approx 5.39 \]

Answer: 5.39

3. Length Between Points (−1, 6) and (5, −2)

Using the distance formula: For points \( (-1, 6) \) and \( (5, -2) \): \[ d = \sqrt{(5 - (-1))^2 + (-2 - 6)^2} = \sqrt{(5 + 1)^2 + (-8)^2} = \sqrt{6^2 + (-8)^2} = \sqrt{36 + 64} = \sqrt{100} = 10 \]

Answer: 10

4. Length Between Points (−2, −1) and (2, 4)

Using the distance formula: For points \( (-2, -1) \) and \( (2, 4) \): \[ d = \sqrt{(2 - (-2))^2 + (4 - (-1))^2} = \sqrt{(2 + 2)^2 + (4 + 1)^2} = \sqrt{4^2 + 5^2} = \sqrt{16 + 25} = \sqrt{41} \approx 6.40 \]

Answer: 6.40

5. Length Between Points (2, -3) and (5, 5)

Using the distance formula: For points \( (2, -3) \) and \( (5, 5) \): \[ d = \sqrt{(5 - 2)^2 + (5 - (-3))^2} = \sqrt{(3)^2 + (5 + 3)^2} = \sqrt{3^2 + 8^2} = \sqrt{9 + 64} = \sqrt{73} \approx 8.54 \]

Answer: 8.54

Summary of Answers

  1. 2.83
  2. 5.39
  3. 10
  4. 6.40
  5. 8.54

Feel free to ask if there’s anything else!

wait idk for the last one because it said i didnt do it and CHANGED MY WORK?!?!

heres the new..

Use the image to answer the question. A map shows a grid 17 units across and 12 units high, superimposed over shapes that represent streets and buildings. A key lists buildings located in Washington D.C. that correspond to points on the grid. Point A represents the White House. It is located at 4 units across from the left, and 3 units down from the top. Point B represents the Washington Monument, located at 5 units across and 9 units down. Point C represents the Natural History Museum, and is located at approximately 8 units across and 8 units down. Point D represents the Smithsonian, and is located at 10 units across and 10 units down. Point E represents the National Portrait Gallery, and is located at 12 units across and 3 units down. Point F represents the National Gallery of Art, and is located at 14 units across and 8 units down. A scale shows 200 feet and 200 meters.Find the length between landmark A and landmark E . (1 point)

2. Use the image to answer the question.A map shows a grid 17 units across and 12 units high, superimposed over shapes that represent streets and buildings. A key lists buildings located in Washington D.C. that correspond to points on the grid. Point A represents the White House. It is located at 4 units across from the left, and 3 units down from the top. Point B represents the Washington Monument, located at 5 units across and 9 units down. Point C represents the Natural History Museum, and is located at approximately 8 units across and 8 units down. Point D represents the Smithsonian, and is located at 10 units across and 10 units down. Point E represents the National Portrait Gallery, and is located at 12 units across and 3 units down. Point F represents the National Gallery of Art, and is located at 14 units across and 8 units down. A scale shows 200 feet and 200 meters.Find the length between landmark B and F . Round the answer to the nearest hundredth, if necessary.

3. Use the image to answer the question.A graph shows four quadrants with the x-axis and y-axis both ranging from negative 10 to positive 10 in increments of 1. Unlabeled points are plotted at left parenthesis negative 6 comma 8 right parenthesis, left parenthesis 4 comma 8 right parenthesis, left parenthesis 4 comma negative 3 right parenthesis, and left parenthesis negative 6 comma negative 3 right parenthesis. A straight line joins the four points forming a rectangle. What is the length of the diagonal of the rectangle? Round your answer to the nearest hundredth, if necessary.

4. Find the distance between (2, 3)
(
2
,

3
)
and (−4, −9)
(
−
4
,

−
9
)
. Round your answer to the nearest hundredth, if necessary.(1 point)

5. Find the distance between (−8, −3)
(
−
8
,

−
3
)
and (−2, −5)
(
−
2
,

−
5
)
. Round your answer to the nearest hundredth, if necessary.(1 point)

Let’s solve these problems step by step using the distance formula, which is expressed as follows:

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

1. Length Between Landmark A (White House) and Landmark E (National Portrait Gallery)

  • Coordinates of Landmark A: \( (4, 3) \)
  • Coordinates of Landmark E: \( (12, 3) \)

Using the distance formula: \[ d = \sqrt{(12 - 4)^2 + (3 - 3)^2} = \sqrt{(8)^2 + (0)^2} = \sqrt{64} = 8 \]

Answer: 8 (units)

2. Length Between Landmark B (Washington Monument) and Landmark F (National Gallery of Art)

  • Coordinates of Landmark B: \( (5, 9) \)
  • Coordinates of Landmark F: \( (14, 8) \)

Using the distance formula: \[ d = \sqrt{(14 - 5)^2 + (8 - 9)^2} = \sqrt{(9)^2 + (-1)^2} = \sqrt{81 + 1} = \sqrt{82} \approx 9.06 \]

Answer: 9.06 (units)

3. Length of the Diagonal of the Rectangle

The rectangle's vertices are given by these points:

  • \( (-6, 8) \)
  • \( (4, 8) \)
  • \( (4, -3) \)
  • \( (-6, -3) \)

To find the length of the diagonal, we can use two opposite corners. Let’s take \( (-6, 8) \) and \( (4, -3) \).

Using the distance formula: \[ d = \sqrt{(4 - (-6))^2 + (-3 - 8)^2} = \sqrt{(4 + 6)^2 + (-3 - 8)^2} = \sqrt{(10)^2 + (-11)^2} \] \[ = \sqrt{100 + 121} = \sqrt{221} \approx 14.87 \]

Answer: 14.87 (units)

4. Distance Between Points \( (2, 3) \) and \( (-4, -9) \)

Using the distance formula: \[ d = \sqrt{(-4 - 2)^2 + (-9 - 3)^2} = \sqrt{(-6)^2 + (-12)^2} = \sqrt{36 + 144} = \sqrt{180} \approx 13.42 \]

Answer: 13.42 (units)

5. Distance Between Points \( (-8, -3) \) and \( (-2, -5) \)

Using the distance formula: \[ d = \sqrt{(-2 - (-8))^2 + (-5 - (-3))^2} = \sqrt{(-2 + 8)^2 + (-5 + 3)^2} = \sqrt{(6)^2 + (-2)^2} \] \[ = \sqrt{36 + 4} = \sqrt{40} \approx 6.32 \]

Answer: 6.32 (units)

Summary of Answers

  1. 8
  2. 9.06
  3. 14.87
  4. 13.42
  5. 6.32

Feel free to ask if you need further clarification or assistance!