Question

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 88442.832.834.24

Answer 1

To find the length of the diagonal of the rectangle formed by points A, B, C, and D, we can use the Pythagorean Theorem.

The coordinates of the points are:

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

In this case, the rectangle has the following dimensions:

• Length (along the x-axis) from A to B or from D to C = 3 - 1 = 2 units
• Height (along the y-axis) from A to D or from B to C = 4 - 2 = 2 units

Now we can use the Pythagorean Theorem to find the diagonal (d):

\[ d = \sqrt{(length^2) + (height^2)} = \sqrt{(2^2) + (2^2)} = \sqrt{4 + 4} = \sqrt{8} = 2\sqrt{2} \]

Calculating \(2\sqrt{2}\):

\[ \sqrt{2} \approx 1.414 \] \[ 2\sqrt{2} \approx 2 \times 1.414 = 2.828 \]

So, rounding this to the nearest hundredth, the length of the diagonal is approximately 2.83.

The correct response is 2.83.