Triangle def has vertices d(−4, 1), e(2, 3), and f(2, 1) and is dilated by a factor of 3 using the point (1, 1) as the point of dilation. the dilated triangle is named δd'e'f'. what are the coordinates of the vertices of the resulting triangle?

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Step-by-step explanation:

Since the center of dilation is not at the origin, we can use the following formula in order to find the coordinates of the vertices of the triangle D'E'F':

Where "O" is the center of dilation at (a,b) and "k" is the scale factor.

In this case you can identify that:

Therefore, susbtituting values into the formula shown above, you get that the coordinates ot the resulting triangle D'E'F, are the following:

Vertex D' →

Vertex E' →

Vertex F' →

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