Example 8 - Chapter 7 Class 10 Coordinate Geometry

Transcript

Example 8 Find the coordinates of the points of trisection (i.e., points dividing in three equal parts) of the line segment joining the points A(2, 2) and B( 7, 4). Let the given points be A(2, 2) & B( 7, 4) P & Q are two points on AB such that AP = PQ = QB Let k = AP = PQ = QB Hence comparing AP & PB AP = m PB = PQ + QB = k + k Hence, Ratio between AP & PB = AP/PB = /2 = 1/2 Thus P divides AB in the ratio 1:2 Finding P Let P(x, y) Hence, m1 = 1 , m2 = 2 And for AB x1 = 2 , x2 = 2 y1 = 7 , y2 = 4 Hence, point P is P(x, y) = P( 1, 0) Similarly, Point Q divides AB in the ratio AQ & QB = / = ( + )/ = ( + )/ = 2 / = 2/1 = 2 : 1 Finding Q Let Q be Q(x, y) m1 = 2 , m2 = 1 x1 = 2 , x2 = 2 y1 = 7 , y2 = 4 Hence, point Q is Q(x, y) = Q( 4, 2)