To find the length between the two points (-2, -1) and (2, 4), we can use the Pythagorean Theorem.
First, we find the difference in x-coordinates by subtracting the x-coordinate of the first point from the x-coordinate of the second point:
2 - (-2) = 4
Then, we find the difference in y-coordinates by subtracting the y-coordinate of the first point from the y-coordinate of the second point:
4 - (-1) = 5
Now, we have the lengths of the two legs of a right triangle. To find the length of the hypotenuse (which is the distance between the two points), we can use the Pythagorean Theorem:
c^2 = a^2 + b^2
where c is the length of the hypotenuse, and a and b are the lengths of the two legs.
Plugging in the values we found:
c^2 = 4^2 + 5^2
c^2 = 16 + 25
c^2 = 41
Taking the square root of both sides to find c:
c = sqrt(41)
Rounding to the nearest hundredth, the length between the two points is approximately 6.40.
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
6:40
6:40
41
41
9
9
5.57
1 answer