1. Find the length of a diagonal of a rectangle ABCD with vertices, A (-3,1), B(-1,3), C(3,-1) and D (1,-3).
A) 5.7
B) 6.3
C) 3.2 *
D) 4.5
To find the length of the diagonal of a rectangle, we can use the distance formula between its opposite vertices.
Let's use the distance formula between points A(-3, 1) and C(3, -1):
d = √[(x2 - x1)^2 + (y2 - y1)^2]
Substituting the values, we have:
d = √[(3 - (-3))^2 + (-1 - 1)^2]
= √[6^2 + (-2)^2]
= √[36 + 4]
= √[40]
= 2√10
Therefore, the length of the diagonal of the rectangle is 2√10.
The correct answer is not provided in the given options.
To find the length of the diagonal of a rectangle, we can use the distance formula between two points.
The distance formula is given by:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Let's label the coordinates of points A, B, C, and D:
A(-3, 1)
B(-1, 3)
C(3, -1)
D(1, -3)
Now, we can find the length of the diagonal by calculating the distances between opposite vertices of the rectangle. In this case, we need to find the distance between points A and C (or B and D) because they are opposite vertices.
Using the distance formula, we have:
AC = sqrt((3 - (-3))^2 + (-1 - 1)^2)
= sqrt((6)^2 + (-2)^2)
= sqrt(36 + 4)
= sqrt(40)
= 2 * sqrt(10)
Therefore, the length of the diagonal of the rectangle ABCD is 2 * sqrt(10).
Now, let's look at the answer choices:
A) 5.7
B) 6.3
C) 3.2 *
D) 4.5
We can see that none of the answer choices match 2 * sqrt(10). Therefore, the correct answer is not listed among the given choices.
Kayla, you were given the exact answer of 2√10 by "cyliner",
which is 6.3245553...
which correct to 1 decimals would be 6.3
so .....