Question

points p(5,4) is one of the two points of triesection of tje line segment joining the points a(7,-2) and b(-1,5) near to a .find the coordinates of the other point of triesection

Answer 1

Let the coordinates of P, Q, R and S be (x1, y1); (x2, y2); (x3, y3) and (x4, y4).Now, we have AP = PQ = QR = RS = SB.Now, point P divides the line segment joining points A and B in the ratio of 1 : 4.Now, x1 = 1×7+4×21+4 = 155 = 3y1 = 1×(−4) + 4×61+4 = −4+245 = 205 = 4So, coordinates of P are (3, 4).Now, P is the mid point of AQ.Now, 3 = 2+x22 ⇒x2 = 44 = 6+y22 ⇒y2 = 2So, coordinates of Q are (4, 2).Now,Q is the mid point of PR.Now, 4 = 3+x32 ⇒x3 = 32 = 4+y32 ⇒y3 = 0So, coordinates of R are (3, 0).Now, S is the mid point of RB.x4 = 3+72 = 5y4 = 0−42 = −2So, coordinates of S are (5, −2).
Hope this would clear your doubt about the topic.