In δbcd line n is the perpendicular bisector of bc and line m is the perpendicular bisector of cd which statement describes location of the circumcenter a point 8 b the intersection of line m and cd c the intersection of line n and bc d the intersection of lines n and m

Correct answer is D(the intersection of lines N and M)

Step-by-step explanation:

we Know that  circumcenter of a triangle is  point at which the perpendicular bisectors of the sides of a triangle intersect and which is equidistant from the three vertices. In other words circumcenter of a triangle is the center of the circle which  passes through the vertices of the triangle. It means, any side of the triangle will act as a chord of the circumcircle. Hence the circumcenter of a triangle must lie on the perpendicular bisectors of the sides. therefore the intersection of line N and M must be  circumcenter of the triangle.

I hope this answer will help you

a reflection across the x-axis , followed by the by a reflection across the y-axis , and then a scale dilation of 0.5 .

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1