Posted by Amanda on Sunday, September 18, 2011 at 4:43pm.
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.
maths - geometry - In a space with an orthonormal coordinate system consider the...
math - Quadrilateral ABCD is a square. The coordinates of point A are (3,2), ...
Calculus - Verify please and thank you~ Does the line (x-7)/3=(y+8)/6=(z+4)/5 ...
Calculus and vectors - Verify please and thank you~ 1. Does the line (x-7)/3=(y+...
(act practice) - In the standard (x,y) coordinate plane, point M with ...
Linear Algebra - In 3-space, a plane abc is spanned by three points a, b, c. The...
math - Alright, let's say you want to get from one point to another, in a 3D...
Algebra 2 - how do i do these problems???? Graph each pair of equations in the ...
maths - the mid-point of the line FG is (6,10). if the coordinates of G is (8,14...
Geometry - 1) find the coordinate of the image of point (1,2) translated left 2 ...
For Further Reading