. Point C is on line segment AB so the ratio of AC to CB is 1 to
3. What are the coordinates of
Point ?

Using the section formula, if a point (x,y) divides the line joining the points (x

1

,y

1

) and (x

2

,y

2

) in the ratio m:n, then

(x,y)=(

m+n

mx

2

+nx

1

,

m+n

my

2

+ny

1

)

3AC=CB

CB

AC

=

3

1

Since, A(1,1) and B(2,3) & m:n=1:3

Therefore, we have

C(

m+n

mx

2

+nx

1

,

m+n

my

2

+ny

1

)

(

1+3

(1)(2)+3(1)

,

1+3

(1)(3)+3(1)

)

C→(

4

5

,

2

3

).

the sum of the lengths of any two sides of a triangle is greater than the length of the third side. if you take the three sides of a triangle and add them in pairs, the sum is greater than (not equal to) the third side. if that is not true, then it is not possible to construct a triangle with the given side lengths.

step-by-step explanation: