(-6,-3) (4,-3) (4,8) (-6,8) what is the length of the diagonal of the rectangle. Round to nearest hundredth if necessary
To find the length of the diagonal, we can use the distance formula.
The distance formula is given by:
distance = √((x2 - x1)^2 + (y2 - y1)^2)
Using the given points, let's calculate the distances between opposite corners of the rectangle:
From (-6,-3) to (4,8):
distance = √((4 - (-6))^2 + (8 - (-3))^2)
= √((4 + 6)^2 + (8 + 3)^2)
= √(10^2 + 11^2)
= √(100 + 121)
= √221
≈ 14.87
From (4,-3) to (-6,8):
distance = √((-6 - 4)^2 + (8 - (-3))^2)
= √((-10)^2 + (8 + 3)^2)
= √(100 + 11^2)
= √(100 + 121)
= √221
≈ 14.87
The length of the diagonal is approximately 14.87 (rounded to the nearest hundredth).
To find the length of the diagonal of a rectangle, you 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 diagonal of the rectangle as the hypotenuse of a right triangle. The two sides of the triangle can be determined by the length and width of the rectangle.
The length of the rectangle can be found by taking the difference between the x-coordinates of the two bottom points of the rectangle: 4 - (-6) = 10.
The width of the rectangle can be found by taking the difference between the y-coordinates of the two left points of the rectangle: 8 - (-3) = 11.
Now we can use the Pythagorean theorem:
diagonal^2 = length^2 + width^2
diagonal^2 = 10^2 + 11^2
diagonal^2 = 100 + 121
diagonal^2 = 221
To find the length of the diagonal, we need to take the square root of both sides:
diagonal = sqrt(221)
Using a calculator, we can find that the square root of 221 is approximately 14.87. Therefore, the length of the diagonal of the rectangle is approximately 14.87 units (rounded to the nearest hundredth).
To find the length of the diagonal of the rectangle, we need to find the distance between the two opposite corners of the rectangle. We can use the distance formula to calculate this.
The distance formula is given by:
d = √((x₂ - x₁)² + (y₂ - y₁)²)
Let's label the given points as follows:
Point A: (-6, -3)
Point B: (4, -3)
Point C: (4, 8)
Point D: (-6, 8)
Now we can calculate the length of the diagonal.
Distance AD:
d₁ = √((-6 - (-6))² + (8 - (-3))²)
Simplifying:
d₁ = √(0² + 11²)
d₁ = √(0 + 121)
d₁ = √121
d₁ = 11
Distance BC:
d₂ = √((4 - 4)² + (8 - (-3))²)
Simplifying:
d₂ = √(0² + 11²)
d₂ = √(0 + 121)
d₂ = √121
d₂ = 11
Since we have opposite sides of a rectangle, the lengths AD and BC are equal.
Finally, we calculate the length of the diagonal by using the distances AD or BC:
d = √(d₁² + d₂²)
d = √(11² + 11²)
d = √(121 + 121)
d = √(242)
d ≈ 15.56 (rounded to the nearest hundredth)
Therefore, the length of the diagonal of the rectangle is approximately 15.56 units.