A circle with the equation (x + 4)2 + (y + 2)2 = 36 is reflected over the line x = 1. What is the equation of the image? (x + 4)2 + (y - 2)2 = 36 (x - 6)2 + (y + 2)2 = 36 (x + 6)2 + (y - 2)2 = 36 (x - 4)2 + (y + 2)2 = 36

B

Step-by-step explanation:

Currently, the graph looks like the attachment.

The centre of this circle is at (-4, -2), but when we flip it over the line x = 1 (the blue line on the picture), the centre will become ((1- -4) + 1, -2) = (6, -2).

Look for the equation that matches this center. We want the center (h, k) to be (6, -2), so our equation should look something like:

The answer is B.

(x - 6)² + (y + 2)² = 36

Step-by-step explanation:

Centre before reflection: (-4,-2)

Centre after reflection:

(-4+5+5,-2) = (6,-2)

(x - 6)² + (y + 2)² = 36

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.

21.4 i did it already for s1

step-by-step explanation: