Question

Point A is located at (4, 1) and point B is located at (9, 13) .

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



Enter your answer as decimals in the boxes.

( , )

Answer 1

If we partition the segment in a 4:1 ratio, that means we have 5 parts; 4 to the left of the partition, and 1 to the right. The segment goes from x = 4 to x= 9 which conveniently is a difference of 5. Now we can find the slope so that we can find the y value at x = 8.

Answer: (8, 10.6)

Answer 2

C=(8,10.6)

Explanation:

Given : Line segment AB with coordinate
`A=(x_1,y_1) =(4,1)` and
`B=(x_2,y_2) =(9,13)`

Ratio dives the line segment m:n = 4:1

To find : The coordinates of the point that partitions the directed line segment AB (let C)

Formula used:

`C= ((x_1 n+x_2 m )/(m+n),(y_1 n+y_2 m)/(m+n))`

Place all the values we get,

`C= (((4)(1)+(9)(4))/(4+1),((1)(1)+(13)(4))/(4+1))`

`C= ((4+36)/(5),(1+52)/(5))`

`C= ((40)/(5),(53)/(5))`

`C= (8,10.6)`

Refer the attached graph for clearance.