What are the coordinates of the point on the directed line segment from (-4, - 7) to
(-3,1) that partitions the segment into a ratio of 2 to 3?

The coordinates of the point on the directed line segment from (-4, - 7) to

(-3,1) that partitions the segment into a ratio of 2 to 3 is

or

∴ PointP( x , y ) = ( -3.6, -3.8)

Step-by-step explanation:

Let he points be,

point A( x₁ , y₁) ≡ ( -4 ,-7)

point B( x₂ , y₂) ≡ (-3 , 1)

and Point P( x , y ) be the point on the line Segment AB Divides AB internally in the ratio 2 : 3 i. e m : n

To Find:

Point P( x , y ) = ?

Solution:

IF a Point P divides Segment AB internally in the ratio m : n, then the Coordinates of Point P is given by Section Formula as

Substituting the Given values we get

∴ PointP( x , y ) = ( -3.6, -3.8)

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)

6mm^3 or .6cm^3

      216

      /   \

  36     6

  /   \     /

6     6   6

factor trees are nice.