Translate triangle a by vector (-3/1)to give triangle b. Then rotate your triangle b 180 degrees around the origin to give triangle. Describe fully the single transformation that maps triangle a onto triangle c

Rotation of triangle A across a point (1.5, -0.5) by 180°.

Step-by-step explanation:

Translation of a figure about a vector means translation of a figure by 3 units to the left on x-axis and 1 unit in the positive direction of the y-axis.

Rule for the translation will be,

(x, y) → [(x - 3), (y + 1)]

From the figure attached,

Vertices of the triangle A are A(1, -1), B(1, -4) and C(3, -4)

After translation new image points will be A'(-2, 0), B'(-2, -3), C'(0, -3).

After rotation of these image points 180° about the origin will be,

Rule for the rotation,

(x, y) → (-x, -y)

A'(-2, 0) → A"(2, 0)

B'(-2, -3) → B"(2, 3)

C'(0, -3) → C"(0, 3)

Therefore, A(1, -1) → A"(2, 0) is the single transformation.

Rule for this transformation which maps triangle C to A will be defined by,

Rotation of triangle A across a point (1.5, -0.5) by 180°.

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

step-by-step explanation: