Use scalar multiplication to determine the coordinates of the vertices of the dilated figure. then graph the pre-image and the image of the same coordinate grid.

The coordinates of the vertices of the dilated figure are:

A' is (-2 , 4), B' is (4 , 8), C' is (4 , -2), D' is (-2 , -6) ⇒ the answer is (d)

Step-by-step explanation:

* Lets study the matrix of the dilation

- If we dilate any point by scale factor k we  multiply the

 coordinates of the point by k

- The matrix of the dilation by scale factor k is

* Now lets solve the problem

- We will multiply the matrix of dilation by the matrix of the

  vertices of the quadrilateral

- The dimension of the matrix of the dilation is 2×2 and the

  dimension of the matrix of the vertices of the quadrilateral

  is 2×4 then the dimension of the matrix of the image of the

  quadrilateral is 2×4

∵ The scale factor is 2

∴ The matrix of dilation is

∵ The matrix of the vertices of the quadrilateral is

∴ The image of the quadrilateral is :

∴ The image of point A' is (-2 , 4)

∴ The image of point B' is (4 , 8)

∴ The image of point C' is (4 , -2)

∴ The image of point D' is (-2 , -6)

* The right answer is figure (d)

6mm^3 or .6cm^3

      216

      /   \

  36     6

  /   \     /

6     6   6

factor trees are nice.

center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

we now create space between the x and y terms with parenthesis.

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

we add the squares to both sides.

simplify.

and write the quadratics in factored form.

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.