Find the fourth vertex of the parallelogram abcd whose vertices are a - 2, 3 b 6, 7 c 83
Answers
The answer is d (0,-7) by the property of pallelogram that diagonals of pallelogram bisect each other at O (x,y) by which O(x,y) become mid point of both the diagonals ab and cd due to which coordinate of 0(x,y) become common and (x,y) become equal to which coordinates of bd and ac become equal then we compare x coordinate of one mid point to other x coordinate similiarly in the case of y after that we get the coordinates of fourth vertex. Thankyou if you need or any help related to study asked me
Answer:
The unknown coordinates are (0,-1).
Step-by-step explanation:
Given:
Vertices of the Parallelogram:
A(-2,3)
B(6,7)
C(8,3)
Unknown coordinates of the vertex is point D.
To find the coordinates of Point D we use mid - point formula.
Mid - Point Formula:
Coordinates(x,y) = (x1 + x2)/2 , (y1 + y2)/2
We know that diagonals of a Parallelogram bisect each other. Therefore, the mid - point of AC will be the same as the mid point of BD.
(-2+8) / 2 , (3+3) /2 = (6 +x) / 2 , (7+y) /2
6 / 2 , 6 / 2 = (6 + x) / 2 , (7 + y) / 2
6 / 2 = 6 + x / 2
6 / 2 * 2 = 6 + x
6 = 6 + x
x = 6 - 6 = 0
The x - coordinate is 0.
6 / 2 = 7 + y / 2
7 / 2 * 2 = 6 + y
7 = 6 + y
y = 6 - 7 = - 1
The y - coordinate is - 1.
Therefore, the unknown coordinates are (0,-1).
