Circle A has center of (0, 4) and a radius of 6, and circle B has a center of (−3, 5) and a radius of 24. What steps will help show that circle A is similar to circle B?

Two circles are similar because they have the same shape

Step-by-step explanation:

Circle A with center  ( ( 0 , 4 ) )  and radius  6  has a Cartesian equation

                         ( x − 0 ) 2^2 +  ( y − 4 ) ^2  =  6^ 2

Circle B with center  ( ( − 3 , 5 ) )  and radius  24  has a Cartesian equation

                        (x+3)^2 + (y-5)^2 = 24^2

In the Cartesian plane:

translation (shift) of    ( a , b )  vector

Every coordinate  x  value has  a  added to it; and  every coordinate  y  value has  b  added to it.

Applying a translation of  

→ ( 0 , 4 ) to circle A  gives the circle A' with the equation:

                ( ( x 0 )  −  0 ) ^2  +  ( ( y + 4 ) − 4 )^ 2  =  6^ 2

                            → x ^2  + y^ 2 = 6 ^2

Applying a translation of   → ( 3 , − 5 )  to circle B  gives a circle B' with the equation:

                      ( ( x + 3 ) − 3 )^ 2 + ( ( y − 5 ) + 5 )^ 2 = 24 ^2

Applying a dilation of  4 to the equation of Circle A' gives the circle A'' with equation

                            x ^2  +  y^ 2  =  ( 6 × 4 ) ^2

                               → x^ 2 + y ^2  =  24 ^2

Since the equations for A'' and B' are identical ,

⇒  Circle A and Circle B are similar.

Dilate the figure x4

Step-by-step explanation:

took the test

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw   congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.