Question

What are the coordinates of the point on the directed line segment from (3,-3) to (7,5) thar oartitions the segment into a ratio of 5 to 3?

Answer 1

(x, y) = (5.5, 2)

Step-by-step explanation:

The coordinates of a point that divide the segment from point (x1, y1) to (x2, y2) into a ratio of a:b can be found using the following equations:

`\begin{gathered} x=x_1+(a)/(a+b)(x_2-x_1) \\ y=y_1+(a)/(a+b)(y_2-y_1) \end{gathered}`

So, replacing (x1, y1) by (3, -3), (x2, y2) by (7, 5) and the ratio a:b by 5:3, we get that the coordinates of the point are:

`\begin{gathered} x=3+(5)/(5+3)(7-3) \\ x=3+(5)/(8)(4) \\ x=3+2.5=5.5 \\ y=-3+(5)/(5+3)(5-(-3)) \\ y=-3+(5)/(8)(5+3) \\ y=-3+(5)/(8)(8) \\ y=-3+5=2 \end{gathered}`

Therefore, the coordinates of the point are (x, y) = (5.5, 2)