The Cartesian plane, also known as the coordinate plane, is a two-dimensional graph used to plot points and represent mathematical equations. It is divided into four quadrants and is used to visually represent the relationships between variables. Distances on the Cartesian plane are measured using the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In the Cartesian plane, this theorem is used to calculate the distance between two points by finding the length of the hypotenuse of a right triangle that connects the two points.
To find the distance between two points on the Cartesian plane, you can use the distance formula: d = √((x2 - x1)^2 + (y2 - y1)^2), where (x1, y1) and (x2, y2) are the coordinates of the two points. This formula is derived from the Pythagorean theorem and gives the distance between two points in terms of their x- and y-coordinates.
No, negative distances do not exist on the Cartesian plane. The distance between two points is always positive, as it is the length of a line segment. However, the coordinates of a point can be negative, depending on its position on the plane.
To calculate the distance between a point and a line on the Cartesian plane, you can use the perpendicular distance formula: d = |ax0 + by0 + c| / √(a^2 + b^2), where (x0, y0) is the coordinate of the point and a, b, and c are the coefficients of the equation of the line. This formula gives the shortest distance between the point and the line, measured along a perpendicular line from the point to the line.