Triangle STV was dilated with the origin as the center of dilation to form Triangle S'T'V'. On a coordinate plane, triangles S T V and S prime T prime V prime are shown. Triangle S T V has points (0, 6), (negative 3, negative 6), and (3, negative 6). Triangle S prime T prime V prime has points (0, 2), (negative 1, negative 2) and (1, negative 2). What is the scale factor of the dilation?

The scale factor of the dilation is .

It is given that,

Explanation:

If a figure is dilated with the origin as the center of dilation. Then, the rule of dilation is defined as:

Where, is the scale factor.

Using this rule, we get

The image of (0,6) is (0,2). So,

Thus, the scale factor of the dilation is .

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  1/3

Explanation:

Triangle STV has points at locations

S = (0, 6)

T = (-3, -6)

V = (3, -6)

Triangle S'T'V' has points at locations

S ' = (0, 2)

T ' = (-1, -2)

V ' = (1, -2)

Pick on just one pair of corresponding points. I'll pick on points S and S'

Going from S = (0,6) to S ' = (0, 2), note how the y coordinate has been divided by 3. This is the same as multiplying by 1/3. Therefore, the scale factor is 1/3

We can see this happening with points T and T ' as well

T = (-3, -6) to T ' = (-1, -2) also has each coordinate multiplied by 1/3

The same can be said from V to V' also.

Because the scale factor is 1/3, this means that the side lengths of the image triangle S'T'V' are 1/3 as long as the preimage triangle STV.

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet