To apply the Pythagorean Theorem, we need to find the lengths of the two sides of the triangle formed by the two points and the origin.
Using point A (2, -3), we can see that the length of the horizontal side (x-axis) is 2 units and the length of the vertical side (y-axis) is 3 units.
Using point B (5, 5), we can see that the length of the horizontal side (x-axis) is 5 units and the length of the vertical side (y-axis) is also 5 units.
Now, we can use the Pythagorean Theorem (a^2 + b^2 = c^2) to find the length of the hypotenuse (c) which represents the distance between the two points.
For point A:
a = 2
b = 3
For point B:
a = 5
b = 5
Using the formula:
c = sqrt(a^2 + b^2)
For point A:
c = sqrt(2^2 + 3^2) = sqrt(4 + 9) = sqrt(13) ≈ 3.61
For point B:
c = sqrt(5^2 + 5^2) = sqrt(25 + 25) = sqrt(50) ≈ 7.07
Rounding both answers to the nearest hundredth, we get:
3.61 rounded to the nearest hundredth = 3.62
7.07 rounded to the nearest hundredth = 7.07
Therefore, the length between the two points is approximately 7.07.
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.
(1 point)
Responses
7.62
7.62
11
11
8.54
8.54
73
1 answer
1 answer