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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

8
8

4
4

4.24
4.24

2.83

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 formula is:

\[ c = \sqrt{a^2 + b^2} \]

where:

• \( c \) is the length of the diagonal,
• \( a \) is the length of one side,
• \( b \) is the length of the other side.

From the points:

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

The lengths of the sides of the rectangle can be calculated as follows:

1. Length of side AB (horizontal side):

   • The coordinates of A and B indicate a horizontal distance of \( 3 - 1 = 2 \).

2. Length of side BC (vertical side):

   • The coordinates of B and C indicate a vertical distance of \( 4 - 2 = 2 \).

Now we apply the Pythagorean theorem:

\[ c = \sqrt{(2)^2 + (2)^2} \] \[ c = \sqrt{4 + 4} \] \[ c = \sqrt{8} \] \[ c = 2.83 \] (approximately, when rounded)

Thus, the length of the diagonal is \( 2.83 \).

The correct answer is:

2.83