Given: The area of a parallelogram is 12. A(-1, 3) and B(-2, 4)
To find: Find the other two vertices of the parallelogram.
Let C is (x, y) and A(-1, 3)
Since, AC is bisected at P, y coordinate ( when p = 0)
Then, (y + 3)/2 = 0
y = -3
So, Coordinate of C is (x, -3)
Now, Area of parallelogram ABCD = area of triangle ABC + Area of triangle BAD
Since, 2(Area of triangles) = area of parallelogram
We have, A(-1, 3) B(-2, 4) and C(x, -3)
12 = 5 - x
So, x = -7
Hence, Coordinate of C is (-7, -3)
In the same we will calculate for D
Let D is (x, y) and A(-2, 4)
Since, BD is bisected at Q, y coordinate ( when Q = 0)
Then, (y + 4)/2
y = -4
So, Coordinate of C is (x, -4)
We have, A(-1, 3) B(-2, 4) and C(x, -4)
12 = 6 - x
So, x = -6
Hence, Coordinate of D is (-6, -4)
Hence, C (-7, -3) and D(-6, -4)