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
8
4.24
4.24
4
4
2.83

Answer 1

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

Points:
- A(1, 2)
- B(3, 2)
- C(3, 4)
- D(1, 4)

First, we find the lengths of the sides of the rectangle:
- The length of side AB (horizontal) is the difference in the x-coordinates:
\( |3 - 1| = 2 \).

- The length of side AD (vertical) is the difference in the y-coordinates:
\( |4 - 2| = 2 \).

Now we can use the Pythagorean Theorem to find the length of the diagonal (d):
\[
d = \sqrt{(AB)^2 + (AD)^2}
\]
Substituting the lengths we found:
\[
d = \sqrt{(2)^2 + (2)^2} = \sqrt{4 + 4} = \sqrt{8}
\]

To round this to the nearest hundredth:
\[
d \approx 2.83
\]

Thus, the length of the diagonal is approximately 2.83.

So the correct response is **2.83**.