parallelogram ABCD has vertices A(8,2),B(6,-4),And C(-5,-4).find the coordinates of D.
To find the coordinates of point D in the parallelogram ABCD, we need to understand the properties of a parallelogram.
A parallelogram is a special type of quadrilateral with opposite sides that are equal in length and parallel to each other. In this case, we know that side AB is parallel to side CD and side BC is parallel to side AD.
To find the coordinates of point D, we can follow these steps:
1. Use the coordinates of point B and C to find the slope of side BC.
- Slope = (y2 - y1) / (x2 - x1)
Using B(6, -4) and C(-5, -4):
Slope of BC = (-4 - (-4)) / (6 - (-5))
= 0 / 11
= 0
Since the slope of BC is 0, the line is horizontal.
2. Start from point A and move along the same horizontal line as BC.
- Since BC is horizontal and parallel to AD, we can use the y-coordinate of A and the length of BC to find the y-coordinate of D.
Using A(8, 2) and B(6, -4):
Length of BC = x-coordinate of B - x-coordinate of C
= 6 - (-5)
= 11
The y-coordinate of D is the same as the y-coordinate of A because AD is parallel to BC.
So, y-coordinate of D = 2
3. Find the x-coordinate of D.
- Since AD is parallel to BC, the length of AD is equal to the length of BC.
Using A(8, 2) and B(6, -4):
Length of AD = x-coordinate of A - x-coordinate of B
= 8 - 6
= 2
We can use the x-coordinate of B and the length of AD to find the x-coordinate of D.
x-coordinate of D = x-coordinate of B + Length of AD
= 6 + 2
= 8
So, the coordinates of point D are (8, 2).
A = B+(2,6), so
D = C+(2,6) = (-3,2)