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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

6:40
6:40

9
9

5.57
5.57

41

Answer 1

To find the distance between the two points $(-2,-1)$ and $(2,4)$, we can use the Pythagorean Theorem. The distance $d$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by the formula:

$$d=\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}$$

Substituting the values from our points:

• $x_1=-2$, $y_1=-1$
• $x_2=2$, $y_2=4$

Now, calculate the differences:

$$x_2-x_1=2-(-2)=2+2=4$$ $$y_2-y_1=4-(-1)=4+1=5$$

Now substitute these differences back into the distance formula:

$$d=\sqrt{(4{)}^2+(5{)}^2}$$ $$d=\sqrt{16+25}$$ $$d=\sqrt{41}$$

Now, we need to round to the nearest hundredth:

$\sqrt{41}\approx 6.4$ (using a calculator or estimating).

So, rounding to the nearest hundredth, the distance is approximately:

6.40.

From the options provided, the correct response is 6:40.