Question

Point S is on YB. YS:SB=4:1, Y(-10,6) and B(10,1). Find coordinates for point S

A.(-6,5)
B.(-2,4)
C.(2,3)
D.(6,2)

Answer 1

The correct option will be: D. (6, 2)

Explanation:

Point
`S` divides the line segment
`YB` in a ratio of
`4:1`

Given that,
`Y(-10, 6)` and
`B(10, 1)`

If a point
`(x,y)` divides a line segment with endpoints as
`(x_(1), y_(1))` and
`(x_(2), y_(2))` in a ratio of
`m:n` , then...........

`(x, y)= ((mx_(2)+nx_(1))/(m+n),(my_(2)+ny_(1))/(m+n))`

Here,
`(x_(1), y_(1))=(-10,6)` and
`(x_(2), y_(2))=(10,1)`

Also,
`m:n=4:1`

Now plugging the values, we will get........

`x=(4(10)+1(-10))/(4+1)= (40-10)/(5)= (30)/(5)=6 \\ \\ \\ y=(4(1)+1(6))/(4+1)= (4+6)/(5)= (10)/(5)=2`

So, the coordinates for point S will be: (6, 2)