Question

determine the two points of trisection p1(x_1,y_1) and p2(x_2,y_2) of the line segment joining A(3,-1) and B(9,7)
if possible can you show me some detailed explanation and some illustration.

Answer 1

Determine the two points of trisection $p1(x_1, y_1)$ and $p2(x_2, y_2)$ of the line segment joining $A(3, -1)$ and $B(9, 7)$ .

Solution:

$$X 1 = X a + \frac {1}{3} (X b - X a) = 3 + \frac {1}{3} (9 - 3) = 5$$ $$Y 1 = Y a + \frac {1}{3} (Y b - Y a) = - 1 + \frac {1}{3} (7 - (- 1)) = 1 \frac {2}{3}$$ $$X 2 = X a + \frac {2}{3} (X b - X a) = 3 + \frac {2}{3} (9 - 3) = 7$$ $$Y 2 = Y a + \frac {2}{3} (Y b - Y a) = - 1 + \frac {2}{3} (7 - (- 1)) = 4 \frac {1}{3}$$

Answer:

$$p 1 \left(5, 1 \frac {1}{3}\right); p 2 \left(7, 4 \frac {1}{3}\right)$$

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