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. Data points marked are point A at left parenthesis 2 comma negative 3 right parenthesis, and point B at left parenthesis 5 comma 5 right parenthesis.
Apply the Pythagorean Theorem to find the length between the two points. Round your answer to the nearest hundredth, if necessary.
A. 73
B. 7.62
C. 11
D. 8.54
Using the Pythagorean Theorem, the length between two points (x1, y1) and (x2, y2) can be found using the formula:
distance = sqrt((x2-x1)^2 + (y2-y1)^2)
In this case, point A has coordinates (2, -3) and point B has coordinates (5, 5).
Plugging the values into the formula, we get:
distance = sqrt((5-2)^2 + (5-(-3))^2)
= sqrt(3^2 + 8^2)
= sqrt(9 + 64)
= sqrt(73)
Rounding the answer to the nearest hundredth, the length between the two points is approximately 8.54.
Therefore, the correct answer is D) 8.54.
To find the length between points A and B, 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, we can consider the line connecting points A and B as the hypotenuse, and the x and y coordinates as the other two sides of the triangle.
The x-coordinate of point A is 2 and the x-coordinate of point B is 5. So, the length of the horizontal side of the triangle is 5 - 2 = 3.
The y-coordinate of point A is -3 and the y-coordinate of point B is 5. So, the length of the vertical side of the triangle is 5 - (-3) = 8.
Now, we can use the Pythagorean Theorem to find the length between the two points:
Length^2 = 3^2 + 8^2
Length^2 = 9 + 64
Length^2 = 73
Taking the square root of both sides, we find:
Length ≈ 8.54
Therefore, the length between points A and B is approximately 8.54. Rounded to the nearest hundredth, the answer is D) 8.54.
To find the length between two points using the Pythagorean Theorem, we need to use the formula:
c = sqrt(a^2 + b^2)
where 'c' is the length between the two points, and 'a' and 'b' are the differences in the x and y coordinates of the two points, respectively.
In this case, point A is (2, -3), and point B is (5, 5).
a = 5 - 2 = 3
b = 5 - (-3) = 8
Now, substitute these values into the formula to calculate the length 'c':
c = sqrt (3^2 + 8^2)
c = sqrt (9 + 64)
c = sqrt(73)
Rounding the answer to the nearest hundredth, the length between the two points is approximately 8.54.
Therefore, the correct answer is D. 8.54.