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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

2.83
2.83

4
4

4.24

Answer 1

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

The distance between points A and B can be found by calculating the difference in their x-coordinates and y-coordinates:

x-coordinate difference: 3 - 1 = 2
y-coordinate difference: 2 - 2 = 0

The distance between points A and B is therefore 2 units.

Similarly, the distance between points B and C is:

x-coordinate difference: 3 - 3 = 0
y-coordinate difference: 4 - 2 = 2

The distance between points B and C is also 2 units.

Since the rectangle formed by points A, B, C, and D is a square, the diagonal of the square has the same length as the distance between points A and B.

Therefore, the length of the diagonal of the square is 2 units.