apply the pythagorean theorem to find the length between the two points (4,2) (-2, -1). round your answer to the nearest hundredth if necessary
To apply the Pythagorean theorem, we need to find the distances along the x-axis and y-axis between the two points.
The distance along the x-axis is given by the difference in x-coordinates:
x2 - x1 = -2 - 4 = -6
The distance along the y-axis is given by the difference in y-coordinates:
y2 - y1 = -1 - 2 = -3
Now we can use these distances to apply the Pythagorean theorem and find the length between the two points:
Length = √((-6)^2 + (-3)^2)
= √(36 + 9)
= √45
≈ 6.71 (rounded to the nearest hundredth)
To find the length between two points (x1, y1) and (x2, y2) using the Pythagorean theorem, follow these steps:
Step 1: Identify the coordinates of the two points.
Given:
Point 1: (x1, y1) = (4, 2)
Point 2: (x2, y2) = (-2, -1)
Step 2: Calculate the differences between the x-coordinates and y-coordinates.
Difference in x-coordinates: x2 - x1 = -2 - 4 = -6
Difference in y-coordinates: y2 - y1 = -1 - 2 = -3
Step 3: Apply the Pythagorean theorem to calculate the length.
Length = √[ (Difference in x-coordinates)^2 + (Difference in y-coordinates)^2 ]
= √[ (-6)^2 + (-3)^2 ]
= √[ 36 + 9 ]
= √45
≈ 6.70 (rounded to the nearest hundredth)
Therefore, the length between the two points (4, 2) and (-2, -1) is approximately 6.70.
To apply the Pythagorean theorem to find the length between two points, we need to follow these steps:
Step 1: Identify the coordinates of the two points.
Given points:
Point A: (4,2)
Point B: (-2, -1)
Step 2: Determine the horizontal and vertical distances between the points.
To find the horizontal distance, subtract the x-coordinates:
Horizontal distance (dX) = x-coordinate of Point B - x-coordinate of Point A
= -2 - 4
= -6
To find the vertical distance, subtract the y-coordinates:
Vertical distance (dY) = y-coordinate of Point B - y-coordinate of Point A
= -1 - 2
= -3
Step 3: Square the horizontal and vertical distances.
Square the horizontal distance (dX^2) = (-6)^2 = 36
Square the vertical distance (dY^2) = (-3)^2 = 9
Step 4: Add the squared distances.
Sum of squared distances (d^2) = dX^2 + dY^2
= 36 + 9
= 45
Step 5: Take the square root of the sum to find the length between the points.
Length (d) = √(d^2)
= √45
≈ 6.71 (rounded to the nearest hundredth)
Therefore, the length between the two points (4,2) and (-2, -1) is approximately 6.71 when rounded to the nearest hundredth.