Parallelogram with coordinates

In summary, to find the coordinates of point D in parallelogram ABCD with given vertices A(2,4), B(5,7), and C(12,8), one can use the formula x=(x1+kx2)/(1+k) and y=(y1+ky2)/(1+k) where k is a ratio. The diagonals of a regular parallelogram bisect each other, so one can first find the coordinates of the point where the diagonals intersect, and then use the above formula to find the coordinates of point D. In this case, the coordinates of D are (9,5).
  • #1
Physicsissuef
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Homework Statement



Parallelogram ABCD is given, with A(2,4), B(5,7), C(12,8). Find the coordinates of D(x,y).

Homework Equations





The Attempt at a Solution



Sorry but, I don't have any idea.
 
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  • #2
here it is a hint, although you haven't shown any work at all! do u know how to find the end points C(x2,y2) of a segment if you are given the first point say A(x1,y1), and another point in the segment say B(x,y), and a ratio, say k. ? well the formula is

x=(x1+kx2)/(1+k), same for y.
in your problem, you probably know that the diagonals of a regular paralelogram bisect each other.. so what u have to do is first find the coordinates of the point where the diagonals bisect each other, and then you will end up with an idenitcal problem that i explained above!
 
  • #3
sutupidmath said:
here it is a hint, although you haven't shown any work at all! do u know how to find the end points C(x2,y2) of a segment if you are given the first point say A(x1,y1), and another point in the segment say B(x,y), and a ratio, say k. ? well the formula is

x=(x1+kx2)/(1+k), same for y.
in your problem, you probably know that the diagonals of a regular paralelogram bisect each other.. so what u have to do is first find the coordinates of the point where the diagonals bisect each other, and then you will end up with an idenitcal problem that i explained above!

Thank you very much. It helped. D(9,5)
 
  • #4
It looks fine, although i personally haven't checked it!
 

Related to Parallelogram with coordinates

1. What is a parallelogram with coordinates?

A parallelogram with coordinates is a geometric shape that has four sides and four angles, where opposite sides are parallel and equal in length. The coordinates refer to the points on a coordinate plane that make up the shape.

2. What are the properties of a parallelogram with coordinates?

A parallelogram with coordinates has several properties, including: opposite sides are parallel and equal in length, opposite angles are congruent, consecutive angles are supplementary, and the diagonals bisect each other.

3. How do you find the area of a parallelogram with coordinates?

To find the area of a parallelogram with coordinates, you can use the formula A = base x height, where the base is the length of one of the sides and the height is the distance between that side and its parallel side. The base and height can be found by using the coordinates of the vertices.

4. Can a parallelogram with coordinates have a negative area?

No, a parallelogram with coordinates cannot have a negative area. The area of a shape is always a positive value, and a parallelogram with coordinates can have a negative length for one of its sides, but the area will still be positive.

5. How is a parallelogram with coordinates different from a regular parallelogram?

A parallelogram with coordinates is different from a regular parallelogram in that it is defined by its coordinates on a coordinate plane, whereas a regular parallelogram is defined by its side lengths and angles. However, a parallelogram with coordinates will still have the same properties as a regular parallelogram.

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