Point B is 1/3 of the way from A to C. What are the coordinates of C? A = (-4 , -7)
B = (12 , 5)

C=(44,29).

Step-by-step explanation:

The given points are A = (-4 , -7)  and B = (12 , 5).

It is given that Point B is 1/3 of the way from A to C.

AB:AC=1:3

AB:BC=AB:(AC-AB)=1:(3-1)=1:2

It means point B divides the line segment AC in 1:2.

Let coordinates of C are (a,b).

Section formula: If a point divides a line segment in m:n, then

Using section formula, we get

On comparing both sides, we get

Therefore, the coordinates of C are (44,29).

A and C

Step-by-step explanation:

To determine which events are equal, we explicitly define the elements in each set builder.

For event A

A={1.3}

for event B

B={x|x is a number on a die}

The possible numbers on a die are 1,2,3,4,5 and 6. Hence event B is computed as

B={1,2,3,4,5,6}

for event C

Hence the set c is C={1,3}

and for the set D {x| x is the number of heads when six coins re tossed }

In the tossing a six coins it is possible not to have any head and it is possible to have head ranging from 1 to 6

Hence the set D can be expressed as

D={0,1,2,3,4,5,6}

In conclusion, when all the set are compared only set A and set C are equal