# Thread: find 4th coordinate of parallelogram

1. ## find 4th coordinate of parallelogram

How do I find the x and y values algebraically of the fourth coordinate of a parallelogram if I know the other 3 points?

TYIA

2. Originally Posted by hello
How do I find the x and y values algebraically of the fourth coordinate of a parallelogram if I know the other 3 points?

TYIA
Hi

If you know the coordinates of A, B, C and you want to find the coordinates of D such that ABCD is a parallelogram then you can use the vector relation
$\overrightarrow{AB} = \overrightarrow{DC}$ which leads to

$x_B - x_A = x_C - x_D$

$y_B - y_A = y_C - y_D$

from which you can find the coordinates of D

3. thanks for the quick response

### forth coordinate

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