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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

2.83
2.83

8
8

4.24
4.24

4

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 rectangle's width (distance between points A and B) and height (distance between points A and D) can be calculated as follows:

• Distance between points A(1, 2) and B(3, 2):
  Width = 3 - 1 = 2

• Distance between points A(1, 2) and D(1, 4):
  Height = 4 - 2 = 2

Now, we can calculate the diagonal \(d\) using the Pythagorean Theorem:

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

Calculating \(2\sqrt{2}\), we find:

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

Rounding to the nearest hundredth, we get:

\[ 2.83 \]

Thus, the length of the diagonal is 2.83.