If center of dilation is D (-1, -1) and the coordinates for triangle ABC are A(0, -2), B(2, -4), and C(3, -1), then what are the coordinates of triangle A'B'C' after a dilation with a scale factor of 2?

A'(1,-3), B'(7,-1) and C'(5,-7).

Step-by-step explanation:

Given,

The coordinates of the triangle ABC are,

A(0, -2), B(2, -4), and C(3, -1)

If a point (x,y) is dilated about a point (p,q) with a scale factor k,

Then the dilation rule is,

Here, the triangle ABC with coordinates A(0, -2), B(2, -4), and C(3, -1) is dilated with scale factor 2 about a point (-1,-1) to form triangle A'B'C'.

That is, k = 2, p = -1, q = -1

Then,

Similarly,

Therefore, the coordinates of triangle A'B'C' are,

A'(1,-3), B'(5,-7) and C'(7,-1)

step-by-step explanation:

because 1/3 is a fraction. we can tell because there is a divisor symbol between the 1 and the 3. if we were to add 2 fractions together, we would add the numerators, which is the number on top, but not the denominators, which is the number on the bottom

1/3+1/3=2/3

hope this !

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.