In parallelogram ABCD, A (0,0),B(a,b)and D(c,0)are three of it's vertices, what are the coordinates of C in terms of a,b,c

To find the coordinates of point C, we need to understand some properties of a parallelogram.

In a parallelogram, opposite sides are parallel. This means that the slope of one side is equal to the slope of the other side.

We can find the slope of line AB using the formula:

slope AB = (y2 - y1) / (x2 - x1)

Using the points A (0,0) and B (a,b), the slope AB = (b - 0) / (a - 0) = b/a.

Since CD is parallel to AB, the slope of CD will also be b/a.

Next, we can find the equation of line CD using the slope-intercept form:

y = mx + c

where m is the slope and c is the y-intercept.

For point D (c,0), the equation becomes:

0 = (b/a) * c + c

Simplifying, we get:

0 = (b/a + 1) * c

Since a parallelogram cannot be degenerate, meaning it cannot have zero area, the product of the coefficients must be non-zero. Therefore, we have:

(b/a + 1) * c ≠ 0

From this equation, we can solve for c.

I would use slopes

Let point C be (x,y)
In my diagram , AD || BC , and both are horizontal.
then x-a = c-0
x = c+a

slope AB = slope CD
b/a = y/(x-c)
y = b(x-c)/a
= b(c+a + a)/a
= b(c + 2a)/a