Question

PLEASE HELP!!!!! ME AND MY MATH CREW ARE TRYING TO FIGURE OUT THIS PROBLEM!!!! IT'S A EMERGENCY!!!!!!

Given: Line segment AB,

with point A at (4, 3) and point B at (10, –9).

Point C lies on segment AB,

such that the ratio of AC:CB is 3:1.

Find the coordinates of point C.

Question 8 options:

(7, –3)


(8.5, –6)


(5.5, 0)


(8, –5)


(9, –7)

Answer 1

a

Explanation:

Answer 2

The coordinates of the point C are:

(8.5,-6)

Explanation:

We know that if a point C(x,y) divides the line segment A(a,b) B(c,d) in the ratio m:n then the coordinates of point C are given by:

`x=(m* c+n* x)/(m+n)\ ,\ y=(m* d+n* b)/(m+n)`

Here we have:

m=3 and n=1

a=4 , b=3 , c=10 and d= -9

Hence, we have:

`x=(3* 10+1* 4)/(3+1)\ ,\ y=(3* (-9)+1* 3)/(3+1)\\\\x=(30+4)/(4)\ ,\ y=(-27+3)/(4)\\\\x=(34)/(4)\ ,\ y=(-24)/(4)\\\\x=8.5\ ,\ y=-6`

Hence, the coordinates of the point C are:

(8.5,-6)