#16 write the equation of the circle

need

equation of circle is given as

where (h,k) is center of cirlce and r is radius.

so lets figure out it from graph.

as we can see in graph center is at ( -1, 1)

radius is 4 units as shown in graph but we can calculate it. take any point on circle and calculate its distance from center. lets take point (3, 1)

now distance = √((3+1)^2+(1-1)^2)

= √16 = 4

lets put it in equation

(x +1)^2 + (y-1)^2 = 4^2

step-by-step explanation:

this is not a question

for the friend request.

when a figure, such as triangle (xyz) is reflected over the line y = x to create x'y'z' the x-coordinates and y-coordinates of the original image (pre-image) will be reversed for the image. (e.g., (x, y) > (y, x)) this means that the pre-image position of the x- and y-coordinates switch places which in turn provides a mirror like image of the original xyz.  

i notice that when i draw a line segment from x to x', that the points are parallel from each other -- they are exactly across from each other and do not intersect with any other points.  

yes, think i would see the same characteristic if you drew the line segment connecting y with the reflecting line and then y' with the reflecting line because of the essence of reflections. because it is a mirror image, each point was effected the same way which leads me to conclude that they same would apply to y and y'.