Question

Point R is located at (3, 2) and point S is located at (8, 15) .

What are the coordinates of the point that partitions the directed line segment RS¯¯¯¯¯ in a 1:4 ratio?



Enter your answer as decimals in the boxes.

Answer 1

Answer: (4,4.6)

Explanation:

Let M be the point with partition the line segment RS in ration 1:4 and has coordinates (x,y)

Then x coordinate of M =
`(mx_2+nx_1)/(m+n)`

`=(1*8+4*3)/(1+4)`

`=(8+12)/(1+4)=(20)/(5)=4`

Now, y coordinate of M =
`(my_2+ny_1)/(m+n)`

`=(1*15+4*2)/(1+4)`

`=(15+8)/(1+4)=(23)/(5)=4.6`

Hence the coordinate of M=(4,4.6)

Answer 2

The x coordinate will be 3 + 1/(4 + 1) * (the positive difference of the x coordinates) , and the y coordinate will be 2 + 1/(4 + 1) * (the positive difference of the y coordinates)

x coordinate = 3 + 1/5(8 - 3) = 3 + 5/5 = 4

y coordinate = 2 + 1/5(15 - 2) = 2 + 13/5 = 4.6

So the new coordinates are ( 4 , 4.6 )