SUMMARY
The point (-1/2, -2) is equidistant from the lines 2x - 3y + 4 = 0 and 6x + 4y - 7 = 0, which are perpendicular to each other. To prove this, calculate the distance from the point to each line using the formula |Ax + By + C| / √(A² + B²). The distances will be equal due to the geometric properties of perpendicular lines, where the dropped perpendicular from the point to one line is parallel to the other line.
PREREQUISITES
- Understanding of the distance formula between a point and a line
- Knowledge of the properties of perpendicular lines
- Familiarity with basic algebraic manipulation
- Ability to interpret linear equations in standard form
NEXT STEPS
- Learn how to apply the distance formula |Ax + By + C| / √(A² + B²) for different points and lines
- Study the geometric implications of perpendicular lines in coordinate geometry
- Explore the concept of equidistance in relation to lines and points
- Investigate the relationship between parallel and perpendicular lines in Cartesian coordinates
USEFUL FOR
Students studying geometry, particularly those focusing on coordinate geometry and the properties of lines, as well as educators looking for examples of equidistance in geometric proofs.