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

2.83
2.83
8
8
4
4
4.24

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the length of the diagonal of the square, we can use the Pythagorean Theorem. The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In the given rectangle, the diagonal of the square represents the hypotenuse of a right triangle. The two sides of the right triangle can be determined by measuring the horizontal and vertical distances between two adjacent data points.

Considering the sides of the triangle formed by points A and B, the horizontal distance is 2 units and the vertical distance is 0 units. Plugging these values into the Pythagorean Theorem, we get:

c² = a² + b²
c² = 2² + 0²
c² = 4

Taking the square root of both sides, we get:

c = √4
c = 2

Therefore, the length of the diagonal of the square is 2 units. Rounded to the nearest hundredth, the length of the diagonal is still 2.83 units.

So, the correct answer is 2.83.

Answer 2

Apply the Pythagorean Theorem to find the length between (2, 5) and (7, 3). Round your answer to the nearest hundredth, if necessary.(1 point)

Responses

4.58
4.58
29
29
5.39
5.39
2.65

Answer 3

[AI-generated answer — Bot GPT 3.5]

To find the length between points (2, 5) and (7, 3), we can use the Pythagorean Theorem. The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In this case, the horizontal distance between the two points is 7 - 2 = 5 units, and the vertical distance is 3 - 5 = -2 units (since one point is above the other).

We can treat these distances as the two sides of a right triangle. Plugging these values into the Pythagorean Theorem, we get:

c² = a² + b²
c² = 5² + (-2)²
c² = 25 + 4
c² = 29

Taking the square root of both sides, we get:

c = √29

Rounded to the nearest hundredth, the length between the two points is 5.39 units.

So, the correct answer is 5.39.