what is the inverse of the transformation:
dilate δabc by a scale factor of 2
a) rotate δabc 90 degrees b) reflect δabc across the x-axis c) dilate δabc by a scale factor of 4 d) dilate δabc by a scale factor of 1 2

D) dilate ΔABC by a scale factor of 1/2

Step-by-step explanation:

Inverse of anything means the reverse or opposite of it.

Here, its given -

dilate ΔABC by a scale factor of 2.

Means double the scale factor. So, its inverse will be half the scale factor.

D: dilate ΔABC by a scale factor of 1/2.

Its like we have been given to multiply something by 2, but we have to apply inverse of it. That will be divide that thing by 2.

The radius is 2 units.

Step-by-step explanation:

x^2 + y^2 + 8x − 6y + 21 = 0

Convert this to the general form (x - a)^2 + (y - b)^2 = r^2 by completing the square:

We have:

x^2 + 8x + y^2 - 6y = -21

(x + 4)^2 - 16 + (y - 3)^2 - 9 = -21

(x + 4)^2 + (y - 3)^2 = 4

Comparing with the above general form we see that

r^2 = 4

and therefore r = 2.