What is the length of the diagonal of the rectangle? Round your answer to the nearest hundredth if necessary, when the plot points are (-6,-3) (4,-3) (4,8) (-6,8)
To find the length of the diagonal of a rectangle, we can use the distance formula.
The coordinates of the first point are (-6, -3), and the coordinates of the opposite point are (4, 8). We can use these coordinates to find the distance between these two points.
Using the distance formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
d = sqrt((4 - (-6))^2 + (8 - (-3))^2)
d = sqrt((4 + 6)^2 + (8 + 3)^2)
d = sqrt(10^2 + 11^2)
d = sqrt(100 + 121)
d = sqrt(221)
Rounding to the nearest hundredth, the length of the diagonal of the rectangle is approximately 14.87.
To find the length of the diagonal of a rectangle, you can use the distance formula between two points. The formula is:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Let's find the distance between the opposite corners of the rectangle.
First, let's label the points:
A = (-6, -3)
B = (4, -3)
C = (4, 8)
D = (-6, 8)
Now, we'll calculate the distances using the formula:
a) Distance between points A and C:
d_AC = sqrt((4 - (-6))^2 + (8 - (-3))^2)
= sqrt((10)^2 + (11)^2)
= sqrt(100 + 121)
= sqrt(221)
≈ 14.87
b) Distance between points B and D:
d_BD = sqrt((-6 - 4)^2 + (8 - (-3))^2)
= sqrt((-10)^2 + (11)^2)
= sqrt(100 + 121)
= sqrt(221)
≈ 14.87
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 a rectangle, we can use the distance formula.
Step 1: Identify the coordinates of the opposite vertices of the rectangle. In this case, the opposite vertices are (-6, -3) and (4, 8).
Step 2: Use the distance formula to find the length of the diagonal. The distance formula is given by √((x₂ - x₁)² + (y₂ - y₁)²).
Let's calculate the length of the diagonal:
√((4 - (-6))² + (8 - (-3))²)
√((4 + 6)² + (8 + 3)²)
√(10² + 11²)
√(100 + 121)
√(221)
≈ 14.87
Therefore, the length of the diagonal of the rectangle is approximately 14.87 units, rounded to the nearest hundredth.