SUMMARY
The coordinates of point D are determined through vector equations involving points A(1,3), B(5,1), and C(2,-8). The vectors AB, BC, and AC are calculated as AB = (4,-2), BC = (-3,-9), and AC = (1,-11). The equation AD = Vector BC + (2x) vector AB + (3y) vector AC is established, leading to a system of equations that can be solved for x and y. The final coordinates of D are derived from the solved values of x and y.
PREREQUISITES
- Understanding of vector operations in a Cartesian coordinate system
- Familiarity with solving systems of linear equations
- Knowledge of vector notation and representation
- Basic algebra skills for manipulating equations
NEXT STEPS
- Study vector addition and subtraction in 2D geometry
- Learn methods for solving systems of linear equations, such as substitution and elimination
- Explore applications of vectors in physics and engineering
- Investigate coordinate transformations and their implications in geometry
USEFUL FOR
Students and professionals in mathematics, physics, and engineering who require a solid understanding of vector operations and their applications in determining coordinates in a Cartesian plane.