Question

1. find the coordinates of the point p that lies along the directed segment from a(1,1) to b(7,3) and partitions the segment in the ratio of 1 to 4. 13. find the coordinate of the point p that lies along the directed segment from c(-3,-2) to d(6,1) and partitions the segment in the ratio 2 to 1.

Explanation:

Step1: Calculate x - coordinate of P for problem 12

$x_1 = 1,y_1 = 1,x_2 = 7,y_2 = 3,k=\frac{1}{5}$
$P_x=1+\frac{1}{5}(7 - 1)=1+\frac{6}{5}=\frac{11}{5}$

Step2: Calculate y - coordinate of P for problem 12

$P_y=1+\frac{1}{5}(3 - 1)=1+\frac{2}{5}=\frac{7}{5}$

Step3: Calculate x - coordinate of P for problem 13

$x_1=-3,y_1=-2,x_2 = 6,y_2 = 1,k=\frac{2}{3}$
$P_x=-3+\frac{2}{3}(6+3)=-3 + 6=3$

Step4: Calculate y - coordinate of P for problem 13

$P_y=-2+\frac{2}{3}(1 + 2)=-2+2 = 0$

Answer:

1. $(\frac{11}{5},\frac{7}{5})$
2. $(3,0)$