SOLUTION: ACPB is a parallelogram. Given that A(-3,-2), B(0,9)and C(6,16). Find the co-ordinates of P and the area of ACBP

Question 193036: ACPB is a parallelogram. Given that A(-3,-2), B(0,9)and C(6,16). Find the co-ordinates of P and the area of ACBP
Answer by Edwin McCravy(20056) (Show Source): You can put this solution on YOUR website!
): ACPB is a parallelogram. Given that A(-3,-2), B(0,9)and C(6,16). Find the co-ordinates of P and the area of CBAP

Connect these:

We notice that C is 6 units right of B and 7 units above B
So the 4th vertex of the desired parallelogram will be
6 units right of A and 7 units above A,
Since we want a point 6 units right of (-3,-2), we add 6 units
to its x-coordinate -3 and get -3+6 or 3 for the x-coordinate
of P. And since we want the point to be 7 units above (-3,-2),
we add 7 units to its y-coordinate -2 and get -2+7 or 5 for the y-coordinate
of P.
So the fourth vertex of the parallelogram is P(3,5)

and the parallelogram looks like this:

To find the area of the parallelogram we first split it
into two congruent triangles using diagonal AC.

Then we find the area of triangle ABC by use of this determinant
formula:

where the points are taken counter-colckwise, that is A to C to B

So the area of the parallelogram is twice that or 45.
Edwin
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