Question

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

Answer 1

✬ The points of trisection are (2, -5/3),(0,-7/3) ✬

Step-by-step explanation:

Given: The points of trisection of the line segment joining the points (4,-1)and(-2,-3).

To find: Points of trisection

Solution:-

Required Formula:-

• The point which divides AB = (mx₂+nx₁/m+n, my₂+ny₁/m+n)

❍ Let the point P divides AB in the ratio 1:2 and the point Q divides AB in the ratio 2:1 internally when m:n = 1:2.

Where,

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

Applying the values,

Case 1,

$\\ :\implies\sf{P = \bigg( \frac{1( - 2) + 2(4)}{1 + 2} ,\frac{1( - 3) + 2( - 1)}{1 + 2} } \bigg)\\ \\ :\implies\sf{P = \bigg( \frac{ - 2 + 8}{3}, \frac{ - 3 - 2}{3} \bigg)} \\ \\:\implies\sf{P = \bigg(\frac{6}{3}, \frac{ - 5}{3} \bigg)} \\ \\ :\implies\sf{P = \bigg(2 ,\frac{ - 5}{3} \bigg)}$

Case 2,

Where,

• m:n = 2:1

$\\ :\implies\sf{Q = \bigg(\frac{2( - 2) + 1(4)}{2 + 1} ,\frac{2( - 3) + 1( - 1)}{2 + 1} \bigg)} \\ \\ :\implies\sf{Q = \bigg(\frac{ - 4 + 4}{3}, \frac{ - 6 - 1}{3} \bigg) } \\ \\ :\implies\sf{Q = \bigg(\frac{0}{3} , \frac{ - 7}{3} \bigg) } \\ \\ :\implies\sf{Q = \bigg(0, \frac{ - 7}{3} \bigg) }$

• ∴ The points of trisection are (2,-5/3),(0,-7/3).

Answer 2

Answer:

Please mark me brilliant