Find the distance between (−2, 1) and (4, 3) . Round the answer to the nearest hundredth.
The distance between two points (x1, y1) and (x2, y2) can be found using the distance formula:
d = √[(x2 - x1)^2 + (y2 - y1)^2]
In this case, (x1, y1) = (-2, 1) and (x2, y2) = (4, 3).
d = √[(4 - (-2))^2 + (3 - 1)^2]
= √[(4 + 2)^2 + (3 - 1)^2]
= √[6^2 + 2^2]
= √[36 + 4]
= √40
≈ 6.32
Therefore, the distance between (-2, 1) and (4, 3) is approximately 6.32.
The distance between two points (x1, y1) and (x2, y2) can be found using the distance formula:
d = √[(x2 - x1)^2 + (y2 - y1)^2]
In this case, (x1, y1) = (2, 3) and (x2, y2) = (-4, -9).
d = √[(-4 - 2)^2 + (-9 - 3)^2]
= √[(-6)^2 + (-12)^2]
= √[36 + 144]
= √180
≈ 13.42
Therefore, the distance between (2, 3) and (-4, -9) is approximately 13.42.
The distance between two points (x1, y1) and (x2, y2) can be found using the distance formula:
d = √[(x2 - x1)^2 + (y2 - y1)^2]
In this case, (x1, y1) = (-8, -3) and (x2, y2) = (-2, -5).
d = √[(-2 - (-8))^2 + (-5 - (-3))^2]
= √[(-2 + 8)^2 + (-5 + 3)^2]
= √[6^2 + (-2)^2]
= √[36 + 4]
= √40
≈ 6.32
Therefore, the distance between (-8, -3) and (-2, -5) is approximately 6.32.
Find the distance between (2, 3) and (−4, −9) . Round your answer to the nearest hundredth, if necessary.
Find the distance between (−8, −3) and (−2, −5) . Round your answer to the nearest hundredth, if necessary.
Apply the Pythagorean Theorem to find the length between (2, 5) and (7, 3) . Round your answer to the nearest hundredth, if necessary
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 consider the line segment joining the points (2, 5) and (7, 3) as the hypotenuse of a right triangle.
The length of the horizontal side (base) of the triangle is 7 - 2 = 5 units, and the length of the vertical side (height) is 3 - 5 = -2 units (we ignore the negative sign, as we are considering the length).
Using the Pythagorean theorem:
c^2 = a^2 + b^2
c^2 = 5^2 + (-2)^2
= 25 + 4
= 29
Taking the square root of both sides:
c ≈ √29
≈ 5.39
Therefore, the length between (2, 5) and (7, 3) is approximately 5.39.
Apply the Pythagorean Theorem to find the length between (−1, 6) and (5, −2) . Round your answer to the nearest hundredth, if necessary
To find the length between two points, we can use the Pythagorean theorem.
Given the points (-1, 6) and (5, -2), we can consider the line segment joining these points as the hypotenuse of a right triangle.
The length of the horizontal side (base) of the triangle is 5 - (-1) = 6 units, and the length of the vertical side (height) is -2 - 6 = -8 units (we ignore the negative sign, as we are considering the length).
Using the Pythagorean theorem:
c^2 = a^2 + b^2
c^2 = 6^2 + (-8)^2
= 36 + 64
= 100
Taking the square root of both sides:
c ≈ √100
≈ 10
Therefore, the length between (-1, 6) and (5, -2) is approximately 10.
To find the distance between two points in a coordinate plane, you can use the distance formula. The distance formula is derived from the Pythagorean theorem.
The formula to find the distance between two points, (x1, y1) and (x2, y2), is:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Let's use this formula to calculate the distance between (-2, 1) and (4, 3).
First, identify the coordinates:
x1 = -2
x2 = 4
y1 = 1
y2 = 3
Substitute the values into the formula:
Distance = √((4 - (-2))^2 + (3 - 1)^2)
Distance = √((6)^2 + (2)^2)
Distance = √(36 + 4)
Distance = √40
To round the answer to the nearest hundredth, evaluate the square root and round the result:
Distance ≈ √40 ≈ 6.324555
Distance ≈ 6.32 (rounded to the nearest hundredth)
Therefore, the distance between (-2, 1) and (4, 3) is approximately 6.32 units, rounded to the nearest hundredth.