What are the co-ordinates of the centre of a window of size 200 × 300 placed in Cartesian coordinate system such that the lower left corner is at (250,250) ?
Answers
Explanation:
Vectors are usually described in terms of their components in a coordinate system. Even in everyday life we naturally invoke the concept of orthogonal projections in a rectangular coordinate system. For example, if you ask someone for directions to a particular location, you will more likely be told to go 40 km east and 30 km north than 50 km in the direction 37° north of east.
In a rectangular (Cartesian) xy-coordinate system in a plane, a point in a plane is described by a pair of coordinates (x, y). In a similar fashion, a vector →A in a plane is described by a pair of its vector coordinates. The x-coordinate of vector →A is called its x-component and the y-coordinate of vector →A is called its y-component. The vector x-component is a vector denoted by →Ax. The vector y-component is a vector denoted by →Ay. In the Cartesian system, the x and y vector components of a vector are the orthogonal projections of this vector onto the x– and y-axes, respectively. In this way, following the parallelogram rule for vector addition, each vector on a Cartesian plane can be expressed as the vector sum of its vector components:
→A=→Ax+→Ay.
As illustrated in (Figure), vector →A is the diagonal of the rectangle where the x-component →Ax is the side parallel to the x-axis and the y-component →Ay is the side parallel to the y-axis. Vector component →Ax is orthogonal to vector component →Ay.