Question

number 3: big ideas 3.5 (find the coordinates of point P along the directed line segment AB, from A(8,0) to B(3,-2), so that the ratio of AP to PB is 1 to 4)

Answer 1

Point P(x,y) divides the segment AB in the ratio m:n if it has coordinates:

`P(x,y)=(\frac{m_{}x_2+n_{}x_1}{m+n},(my_2+ny_1)/(m+n))`

where A(x1,y1) and B(x2,y2).

In this case we have the ratio 1:4, this means that m=1 and n=4. Plugging this and the coordinates of points A and B we have:

`\begin{gathered} P(x,y)=((1\cdot3+4\cdot8)/(1+4),(1\cdot(-2)+4\cdot(0))/(1+4)) \\ P(x,y)=((3+32)/(5),(-2)/(5)) \\ P(x,y)=((35)/(5),-(2)/(5)) \\ P(x,y)=(7,-(2)/(5)) \end{gathered}`

Therefore the coordinates of the point P are (7,-2/5)