Question

1. Given the points Al-1, 2) and B(7, 8), find the coordinates of the polnt P on the directed line segment JB that partitions AB in the ratio 1:3. Plot P along with segment AB. 10 B 6 (x,y) = (x1+k(x2 - x2),y. +k(y2-y) 2 210182632 2 68 110 2 24 6 8 -10 2. Find the coordinates of P so that P partitions AB in the ratio 5.1 with A(2, 4) and B(8, 10). L 3. Find the coordinates of P so that P partitions AB in the ratio 1 to 3 with A(-5, 4) and B(7,-4). 4. Find the coordinates of P so that P partitions AB in the ratio 3:4 with A(-9, -9) and B(5,-2).

Answer 1

We can find the point with help of the end points and the ratio so:

$\begin{gathered} x=-1+\frac{1}{1+3}(7-(-1)) \\ x=-1+\frac{1}{4}8 \\ x=-1+2 \\ x=1 \end{gathered}$

now for y:

$\begin{gathered} y=2+\frac{1}{1+3}(8-2) \\ y=2+\frac{1}{4}6 \\ y=3.5 \end{gathered}$

So now we can graph it so: