Question

Use the image to answer the question.

A graph shows four quadrants with the x-axis and y-axis both ranging from negative 5 to positive 5 in increments of 1. Unlabeled data points marked are at left parenthesis negative 2 comma negative 1 right parenthesis, and at left parenthesis 2 comma 4 right parenthesis. A straight line joins the two lines with a positive slope.

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

(1 point)
Responses

9
9

5.57
5.57

41
41

6:40

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the length between the two points, we can use the distance formula or apply the Pythagorean theorem.

Let's label the first point as (x₁, y₁) = (-2, -1) and the second point as (x₂, y₂) = (2, 4).

Using the distance formula, the length between the two points is given by:
d = sqrt((x₂ - x₁)² + (y₂ - y₁)²)

Substituting the values, we get:
d = sqrt((2 - (-2))² + (4 - (-1))²)
d = sqrt((2 + 2)² + (4 + 1)²)
d = sqrt(4² + 5²)
d = sqrt(16 + 25)
d = sqrt(41)
d ≈ 6.40

Therefore, the length between the two points is approximately 6.40 units.