STRAIGHT LINES René Descartes ( - ) Fig . MATHEMATICS I. Distance between the points P ( x , y ) and Q ( x , y ) is PQ x – x y – y For example, distance between the points ( , – ) and ( , ) is units. II.
The coordinates of a point dividing the line segment joining the points ( x , y ) and ( x , y ) internally, in the ratio m: n are m m m m , For example, the coordinates of the point which divides the line segment joining A ( , – ) and B (– , ) internally, in the ratio : are given by ( ) and . + . – = . + III.
In particular, if m = n , the coordinates of the mid-point of the line segment joining the points ( x , y ) and ( x , y ) are , IV. Area of the triangle whose vertices are ( x , y ), ( x , y ) and ( x , y ) is For example, the area of the triangle, whose vertices are ( , ), ( , – ) and (– , ) is ( ) ( ) ( )( ) . −− + − Remark If the area of the triangle ABC is zero, then three points A, B and C lie on a line, i.e., they are collinear. In the this Chapter, we shall continue the study of coordinate geometry to study properties of the simplest geometric figure – straight line.
Despite its simplicity, the line is a vital concept of geometry and enters into our daily experiences in numerous interesting and useful ways. Main focus is on representing the line algebraically, for which slope is most essential. . Slope of a Line A line in a coordinate plane forms two angles with the x -axis, which are supplementary.