Question

find the points of trisection of the line segment joining the points (4-,1)(-2,3)​

Answer 1

Answer:

ANSWER

Let P and Q be the points of trisection of line joining the points A(4,1) & B(-2,-3).

Then, AP = PQ = QB

Now, P divides AB in the ratio 1:2 and Q divides AB in the ratio 2:1.

Therefore,

Coordinates of P = (  

3

(−7+4)

​  

,  

3

4−4

​  

)=(−1,0)

Coordinates of Q = (  

3

(−14+2)

​  

,  

3

8−2

​  

)=(−4,2)

Hence, the two points of trisection are P(−1,0) and (−4,2).

Step-by-step explanation:

Answer 2

Answer:

Let the points be A(4,-1) and B(-2,3)

As we have to find the points of trisection of line segment AB, we have to find the two points which divide AB into three parts.

Let the required points be P(a,b) and Q(c,d)

A---------------P---------------Q---------------B

As we can see in the above figure, that point P divides AB by ratio 1 : 2

Thus by section formula we will find point P

m = 1, n = 2, x1 = 4, x2 = (-2), y1 = (-1), y2 = 3

$Section \: formula = ( \frac{m(x2) + n(x1)}{m + n} , \frac{m(y2) + n(y1)}{m + n} ) \\ .°.P(a,b) = ( \frac{1( - 2) + 2(4)}{1 + 2} ,\frac{1(3) + 2( - 1)}{1 + 2} ) \\ .°.P(a,b) = ( \frac{ - 2 + 8}{3} , \frac{3 - 2}{3} ) \\ .°.P(a,b) = ( \frac{6}{3} , \frac{1}{3} ) \\ .°.P(a,b) = (2, \frac{1}{3} )$

As Q divides AB by ratio 2 : 1, it also divides PB by ratio 1 : 1

Thus we can say that Q is midpoint of PB

x1 = 2, x2 = (-2), y1 = 1/3, y2 = 3

$midpoint \: formula = ( \frac{x1 + x2}{2}, \frac{y1 + y2}{2} ) \\ Q(c,d)= (\frac{2 + ( - 2)}{2} , \frac{ \frac{1}{3} + 3}{2} ) \\ Q(c,d)= ( \frac{2 - 2}{2} , \frac{ \frac{1 + 9}{3} }{2} ) \\ Q(c,d)= (0, \frac{ \frac{10}{3} }{2} ) \\ Q(c,d)= (0, \frac{10}{3 \times 2} ) \\ Q(c,d)= (0, \frac{10}{6} ) \\ Q(c,d) = (0, \frac{5}{3} )$