Sophia Alfred

Points A and B are at #(3 ,5 )# and #(6 ,1 )#, respectively. Point A is rotated counterclockwise about the origin by #(3pi)/2 # and dilated about point C by a factor of #3 #. If point A is now at point B, what are the coordinates of point C?

Two circles have the following equations: #(x +3 )^2+(y -1 )^2= 64 # and #(x -7 )^2+(y +2 )^2= 25 #. Does one circle contain the other? If not, what is the greatest possible distance between a point on one circle and another point on the other?

What is the area of an equilateral triangle whose vertices lie on a circle with radius 2?

Two corners of a triangle have angles of #(3 pi ) / 8 # and # pi / 4 #. If one side of the triangle has a length of #1 #, what is the longest possible perimeter of the triangle?

Find the value of a and b.? The polygons are similar, but not necessarily drawn to scale.

Points A and B are at #(4 ,5 )# and #(7 ,2 )#, respectively. Point A is rotated counterclockwise about the origin by #(3pi)/2 # and dilated about point C by a factor of #1/2 #. If point A is now at point B, what are the coordinates of point C?

A triangle has corners at #(2 ,-5 )#, #(-8 ,4 )#, and #(1 ,-3 )#. If the triangle is dilated by a factor of #2/5 # about point #(-1 ,-2 ), how far will its centroid move?

The number of square meters in the total surface area of a right circular cylinder, including the top and bottom, is equal to the number of cubic meters in its volume. If the radius of the cylinder is five times its height, what is its volume?

Circle A has a center at #(3 ,5 )# and a radius of #1 #. Circle B has a center at #(-1 ,1 )# and a radius of #4 #. Do the circles overlap? If not, what is the smallest distance between them?

The area of a square is 81 square centimeters. What is the length of the diagonal?

Circle A has a radius of #1 # and a center of #(8 ,2 )#. Circle B has a radius of #4 # and a center of #(5 ,3 )#. If circle B is translated by #<-2 ,5 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?

How do you use Heron's formula to find the area of a triangle with sides of lengths #3 #, #2 #, and #4 #?

A line passes through #(3 ,6 )# and #(6 ,5 )#. A second line passes through #(4 ,3 )#. What is one other point that the second line may pass through if it is parallel to the first line?

Can a rhombus be a kite?

If 3 times the supplement of an angle is subtracted from 7 times the complement of the angle, the answer is the same as that obtained from trisecting a right angle. What is the supplement of this angle?

A line segment has endpoints at #(9 ,3 )# and #(5 ,4 )#. The line segment is dilated by a factor of #3 # around #(4 ,6 )#. What are the new endpoints and length of the line segment?

A triangle has corners A, B, and C located at #(6 ,4 )#, #(2 ,5 )#, and #(3 , 1 )#, respectively. What are the endpoints and length of the altitude going through corner C?

A conjecture and the two-column proof used to prove the conjecture are shown. Match the expression or phrase to each statement or reason to complete the proof?

Point A is at #(-7 ,-1 )# and point B is at #(2 ,-4 )#. Point A is rotated #pi # clockwise about the origin. What are the new coordinates of point A and by how much has the distance between points A and B changed?

Two corners of a triangle have angles of # (5 pi )/ 12 # and # ( pi ) / 12 #. If one side of the triangle has a length of # 16 #, what is the longest possible perimeter of the triangle?