Sunday

December 21, 2014

December 21, 2014

Posted by **Amanda** on Sunday, September 18, 2011 at 4:43pm.

(b)AC as one of the diagonals

(c)BC as one of the diagonals

- Algebra -
**MathMate**, Sunday, September 18, 2011 at 5:30pmPlot the three points on graph paper or on your calculator.

To insert point D as the 4th point of the parallelogram with AC as diagonal means that you need to find lines L1 parallel to AB passing through C, and L2 parallel to BC passing through A. The intersection of L1 and L2 will be the fourth vertex of the parallelogram.

To find the line L1 parallel to AB passing through C:

Calculate slope of line AB:

slope AB = (yb-ya)/(xb-xa)

=(8-3)/(5-4)=5

L1 passes through C(3,10), so

L1 : y-10 = 5(x-3)

or

L1: y = 5x - 5

Similarly find L2:

slope of BC = (10-8)/(3-5)=2/(-2)=-1

L2 passes through A(4,3), so

L2 : y-3 = -1(x-4), or

L2 : y = -x + 7

The 4th vertex is the intersection of L1 and L2, solved by the system of equations L1 and L2:

y=5x-5...(1)

y=-x+7...(2)

subtract:

6x-12=0, therefore x=2, y=5, or the point D is (2,5).

You can find the fourth vertex of the parallelogram with BC as diagonal in a similar way.

**Answer this Question**

**Related Questions**

Linear Algebra - In 3-space, a plane abc is spanned by three points a, b, c. The...

math - A(4,7) and B(-3,2) are points on a coordinate plane.Find the coordinates ...

Math - 19. Point A(4, 2) is translated according to the rule (x, y) (x + 1, y – ...

maths - geometry - In a space with an orthonormal coordinate system consider the...

geometry CA - Graph quadrilateral ABCD. Then determine the most precise name for...

math:quick help - Let Fn be the nth number in the Fibonacci Sequence. Consider ...

math - Quadrilateral ABCD is a square. The coordinates of point A are (3,2), ...

Coordinate Geometry - Please help!!!!! The points A,B,C,D have coordinates (3,3...

algebra1 - given points : p (2,1) q (-4,2) m(5,3) find the coordinates of a ...

math - Alright, let's say you want to get from one point to another, in a 3D box...