Question

For the Parallelogram, find the coordinates of P without using any new variables.

Answer 1

Answer with explanation:

Properties of Parallelogram

1. Opposite sides are equal and parallel.

2. Diagonals bisect each other.

3. opposite angles are equal.

We will use second property to find coordinates of Vertex P of this parallelogram.

Mid point formula,

The mid point  of line segment joining two points, (a,b) and (c,d)=(x,y) is given by,

  $x=\frac{a+c}{2},y=\frac{b+d}{2}$

Let coordinates of P be (m,n).

$1.\frac{b+c}{2}=\frac{m+a}{2}\\\\ b+c=m+a\\\\ m=b+c-a\\\\2. \frac{d+0}{2}=\frac{0+n}{2}\\\\n=d$

So, Coordinates of vertex P of the parallelogram is (m,n)=(b+c-a,d) .

Option B

Answer 2

I think the answer is b.(C+b-a, d).

Because d is the y-coordinate of the point that is on the left of point P so i guess it makes sense.

Hope this helps :)