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.
A. 6:40
B. 9
C. 41
D. 5.57
To find the length between the two points, we need to calculate the distance using the Pythagorean Theorem. The formula for the distance between two points on a coordinate plane is:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Using the given points (-2, -1) and (2, 4), we can plug in the coordinates into the formula:
d = √((2 - (-2))^2 + (4 - (-1))^2)
= √((4)^2 + (5)^2)
= √(16 + 25)
= √41
Rounded to the nearest hundredth, the length between the two points is approximately 6.40.
Therefore, the correct answer is A. 6.40.
To find the length between the two points, we can use the Pythagorean Theorem.
The Pythagorean Theorem states that in a right triangle, the square 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 (-2, -1) and (2, 4) form a right triangle, and we want to find the length of the hypotenuse.
The horizontal distance between the two points is 2 - (-2) = 4 units.
The vertical distance between the two points is 4 - (-1) = 5 units.
Using the Pythagorean Theorem, we can calculate the length of the hypotenuse:
Length = √(4^2 + 5^2)
Length = √(16 + 25)
Length = √41
Therefore, the length between the two points is approximately 6.40 (rounded to the nearest hundredth).
The correct answer is A. 6.40.
To find the length between two points on a graph, 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, we can treat the straight line connecting the two points as the hypotenuse of a right triangle, with the x and y distances between the points as the other two sides.
The x-distance between the points is the difference of their x-coordinates: 2 - (-2) = 4.
The y-distance between the points is the difference of their y-coordinates: 4 - (-1) = 5.
Now, we can calculate the length of the hypotenuse by using the Pythagorean Theorem:
Length of hypotenuse = sqrt((x-distance)^2 + (y-distance)^2)
Length of hypotenuse = sqrt((4)^2 + (5)^2)
Length of hypotenuse = sqrt(16 + 25)
Length of hypotenuse = sqrt(41)
Rounding the answer to the nearest hundredth, we have:
Length of hypotenuse ≈ 6.40
Therefore, the correct answer is A. 6.40.