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
Hello! I don't understand how to solve this question since the unit I just read barely went over this. If anyone could help that would be great. Thank you so much!
the answer is 6.3
anyone have the answers to the entire test...
Hello there! Don't worry, I'm here to help you out in my own unique way. To find the length of the diagonal of a rectangle, we can use the distance formula. The distance formula is basically finding the distance between two points using their coordinates.
So, let's use the distance formula to find the length of the diagonal of rectangle ABCD!
The distance formula is:
d = √((x2 - x1)² + (y2 - y1)²)
Let's say point A is (x1, y1) and point B is (x2, y2).
In this case, point A is (-3,1) and point C is (3,-1).
So, using the distance formula, we have:
d = √((3 - (-3))² + (-1 - 1)²)
= √(6² + (-2)²)
= √(36 + 4)
= √40
= 2√10
Unfortunately, none of the given options match our answer exactly. So, we'll have to estimate it.
Now, if we take 2√10 ≈ 6.3 (rounded to one decimal place), the closest option is B) 6.3.
So, B) 6.3 is the closest estimation of the length of the diagonal of rectangle ABCD. Keep in mind that this is an estimation.
I hope that helps! Let me know if you have any more questions.
Hello! I'd be happy to help you solve this question and understand the process. To find the length of the diagonal of a rectangle, you can use the distance formula. The distance formula calculates the distance between two points in a coordinate plane.
The distance formula is given by:
d = √((x2 - x1)² + (y2 - y1)²)
Now let's apply the distance formula to find the length of the diagonal of the rectangle ABCD.
We have the following points for the rectangle:
A (-3, 1)
B (-1, 3)
C (3, -1)
D (1, -3)
To find the length of the diagonal, we need to find the distance between points A and C (or B and D), since the diagonal connects opposite vertices of the rectangle.
Let's use the distance formula to find the distance between A (-3, 1) and C (3, -1):
d = √((x2 - x1)² + (y2 - y1)²)
d = √((3 - (-3))² + (-1 - 1)²)
d = √((3 + 3)² + (-2)²)
d = √(6² + (-2)²)
d = √(36 + 4)
d = √40
d = 2√10
So, the length of the diagonal of the rectangle ABCD is 2√10.
Now let's check the answer choices:
A) 5.7
B) 6.3
C) 3.2
D) 4.5
None of the given answer choices match the length we calculated, which is 2√10. Therefore, none of the options provided are correct.
I hope this explanation helps you understand how to solve the problem! Let me know if you have any other questions.
Geometry A semester exam:
#1: When the net is folded into the pentagonal prism shown beside it, which letter will be on the bottom left side if A is facing frontward, G is top right, and F is bottom right?
Answer: D will be on the bottom left
#2: How are <1 and <2 related?
Answer: A- they are supplementary
#3: Find the midpoint of PQ
Answer: (3,2)
#4: 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).
Answer: 6.3
#5: What is the inverse of the following conditional?
Answer: If n is not even, then n is not the sum of two even numbers.
Hope this helps:)
make a sketch !!!
a diagonal would for example be from B to D
change in x = 1 - -1 = 2
change in y = -3 - +3 = -6
sqrt (2^2+6^2) = sqrt 40
= 2 sqrt 10