Posted by Amanda on Sunday, September 18, 2011 at 4:43pm.
Let A(4,3) B(5,8) and C(3,10) be three points in a coordinate plane. Find the coordinates of a point D such that the points ABC and D form a parallelogram with (a)AB as one of the diagonals
(b)AC as one of the diagonals
(c)BC as one of the diagonals
- Algebra - MathMate, Sunday, September 18, 2011 at 5:30pm
Plot 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)
L1 passes through C(3,10), so
L1 : y-10 = 5(x-3)
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:
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
More 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 – ...
- math:quick help - Let Fn be the nth number in the Fibonacci Sequence. Consider ...
- 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 - Quadrilateral ABCD is a square. The coordinates of point A are (3,2), ...
- math - Alright, let's say you want to get from one point to another, in a 3D box...
- 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 ...