Question

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A graph shows quadrant 1 with the x-axis and y-axis ranging from 0 to positive 9. Data points marked are at left parenthesis 3 comma 2 right parenthesis, and left parenthesis 7 comma 8 right parenthesis. A straight line joins the two points forming a positive slope.

Apply the Pythagorean Theorem to find the length between the two points. Round your answer to the nearest hundredth.

(1 point)
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Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the length between the two points (3, 2) and (7, 8), we can use the Pythagorean Theorem.

The distance between two points (x1, y1) and (x2, y2) is given by:

Distance = √((x2 - x1)^2 + (y2 - y1)^2)

Using the coordinates (3, 2) and (7, 8), we have:

Distance = √((7 - 3)^2 + (8 - 2)^2)
= √(4^2 + 6^2)
= √(16 + 36)
= √52
≈ 7.21 (rounded to the nearest hundredth)

Therefore, the length between the two points is approximately 7.21.

Answer 2

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Answer 3

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Answer 4

[AI-generated answer — Explain Bot]

To find the distance between two points in a coordinate plane, 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 other two sides.

In this case, the two points given are (3, 2) and (7, 8). We can consider these two points as the vertices of a right triangle, with the line joining them as the hypotenuse.

To find the length of the hypotenuse, we need to calculate the lengths of the other two sides of the triangle.

The length of the horizontal side can be found by subtracting the x-coordinate of the first point (3) from the x-coordinate of the second point (7):
Horizontal side length = 7 - 3 = 4

The length of the vertical side can be found by subtracting the y-coordinate of the first point (2) from the y-coordinate of the second point (8):
Vertical side length = 8 - 2 = 6

Now, we can use the Pythagorean Theorem to calculate the length of the hypotenuse:
Hypotenuse length = √(Horizontal side length^2 + Vertical side length^2)
Hypotenuse length = √(4^2 + 6^2)
Hypotenuse length = √(16 + 36)
Hypotenuse length = √52

Rounding the result to the nearest hundredth:
Hypotenuse length ≈ 7.21

Therefore, the length between the two given points is approximately 7.21 units.