One side of a parallelogram has endpoints (3, 3) and (1, 7).
What are the endpoints for the side opposite?
(8, 1) and (6, 7)
(6, 1) and (2, 3)
(6, 1) and (8, 5)
(8, 1) and (6, 5)
length of that side = sqrt( (3-1)^2 + sqrt(7-3)^22 )
= sqrt 20
other side must also be sqrt 20
only one works :)
whoops , slopes must be the same
4/-2 = -2
so
a. 6/-2 no
b. 2/-4 no
c. 4/2 no
d. 4/-2 yes
To find the endpoints for the side opposite of a parallelogram, we need to use the properties of a parallelogram.
A parallelogram is a quadrilateral with opposite sides that are parallel and equal in length. One property of parallelograms is that opposite sides are congruent, meaning they have the same length.
Given the endpoints of one side of the parallelogram as (3, 3) and (1, 7), we can use the distance formula to find the length of this side. The distance formula is given by:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Using the distance formula, we find the length of this side to be:
d = sqrt((1 - 3)^2 + (7 - 3)^2)
= sqrt(4 + 16)
= sqrt(20)
= 2 sqrt(5)
Since opposite sides of a parallelogram are congruent, the length of the opposite side will also be 2 sqrt(5).
Now let's examine the answer choices:
(A) (8, 1) and (6, 7):
The length of this side is: sqrt((6 - 8)^2 + (7 - 1)^2) = sqrt(4 + 36) = sqrt(40) ≠ 2 sqrt(5)
So this is not the correct answer.
(B) (6, 1) and (2, 3):
The length of this side is: sqrt((2 - 6)^2 + (3 - 1)^2) = sqrt(16 + 4) = sqrt(20) = 2 sqrt(5)
The length matches the length of the given side, so this could be a valid answer.
(C) (6, 1) and (8, 5):
The length of this side is: sqrt((8 - 6)^2 + (5 - 1)^2) = sqrt(4 + 16) = sqrt(20) = 2 sqrt(5)
The length matches the length of the given side, so this could also be a valid answer.
(D) (8, 1) and (6, 5):
The length of this side is: sqrt((6 - 8)^2 + (5 - 1)^2) = sqrt(4 + 16) = sqrt(20) = 2 sqrt(5)
The length matches the length of the given side, so this is a valid answer.
So, the possible endpoints for the side opposite to (3, 3) and (1, 7) are:
(B) (6, 1) and (2, 3)
(D) (8, 1) and (6, 5)