Which of the following sets of ordered pairs is not a direct variation?

- (0,0) (-2,4) (3, -6)
- (1, 1) (-2, -2) (3,3)
- (10, 2) (15,3) (20,4)
- (0,0) (1,3) (2,4)

The  sets of ordered pairs is NOT a direct variation

- (0,0) (1,3) (2,4)

We know that the set of ordered pair are in  direct variation if they lie on a straight line or we can say if the rate of change is constant.

1)

- (0,0) (-2,4) (3, -6)

From the following set of points we see that we get a straight line as:

y= -2x

Hence , the points are in direct variation.

2)

- (1, 1) (-2, -2) (3,3)

Now, these set of ordered points also satisfy the line as:

y=x

Hence, the points are in direct variation.

3)

- (10, 2) (15,3) (20,4)

Now, these set of ordered points also satisfy the line as:

y=(1/5)x

Hence, the points are in direct variation.

4)

- (0,0) (1,3) (2,4)

We find the rate of change of (0,0) and (1,3) as:

The rate of change of (1,3) and (2,4) is:

As the rate of change is not constant.

Hence, the points are not in direct variation.

Hence,  sets of ordered pairs is NOT a direct variation is:

(0,0) , (1,3), (2,4)

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .

a 4/6 = 9/12   not proportional

step-by-step explanation:

to find which are not proportional, we can use cross products

if it is true, they are proportional.   if it is not true, they are not proportional.

a 4/6 = 9/12

4* 12 = 6*9

48 = 54

not this is not proportional  

b 2/3 = 12/18  

2* 18 = 3 * 12

36 = 36

this is proportional

c 5/4 = 10/8  

5*8 = 4*10

40 = 40

this is proportional

d 7/5 = 35/25

7*25 = 5 * 35

175 = 175

is proportional