the line segment joining the points (3,-4)and (1,2)is trisected at the points Pand Q if the coordinates of Pand - Maths - Coordinate Geometry

Question

the line segment joining the points (3,-4)and (1,2)is trisected
at the points Pand Q if the coordinates of Pand Q are (p,-2) and
(5/3,q) respectively, find the values of p and q

Lalit Mehra · Accepted Answer

Dear Student! Let the given point be A(3, â€“ 4) and B(1, 2)

Given, P and Q trisects AB âˆ´ AP = PQ = QB Now, AP + PQ + QB = AB âˆ´ AP + AP + AP = AB â‡’ 3AP = AB $\Rightarrow AP = \frac{AB}{3} PB = PQ + QB = AP + AP = 2AP = \frac{2}{3} AB$ $\frac{AB}{PB} = \frac{\frac{AB}{3}}{\frac{2 AB}{3}} = \frac{1}{2}$ âˆ´ P divides AB in the ratio 1 : 2 Similarly, Q divides AB in the ratio 2 : 1 Coordinates of the point dividing the line segment joining (x1, y1) and (x2, y2) is the ratio m : n is $(\frac{m x_{2} + n x_{1}}{m + n}, \frac{m y_{2} + n y_{1}}{m + n})$ Coordinates of $P = (\frac{1 \times 1 + 2 \times 3}{1 + 2}, \frac{1 \times 2 + 2 \times (- 4)}{1 + 2})$ $\Rightarrow (p, - 2) = (\frac{7}{3}, - 2) \Rightarrow p = \frac{7}{3}$ Coordinates of $Q = (\frac{2 \times 1 + 1 \times 3}{2 + 1}, \frac{2 \times 2 + 1 \times (- 4)}{2 + 1})$ $\Rightarrow (\frac{5}{3}, q) = (\frac{5}{3}, 0) \Rightarrow q = 0$ Thus, the values of p and q are $\frac{7}{3}$ and 0 respectively Cheers!

the line segment joining the points (3,-4)and (1,2)is trisected at the points Pand Q. if the coordinates of Pand Q are (p,-2) and (5/3,q) respectively, find the values of p and q .