


Violet Aldrich
Geometry teacher | Experienced educator in USA
I'm a passionate educator specializing in geometry, with a degree from Siena College. My dedication to shaping young minds stems from a deep love for the intricacies of geometric concepts. With a firm belief in nurturing curiosity and critical thinking, I guide students to explore the beauty and logic of shapes and spatial relationships. Whether unraveling the mysteries of angles or delving into the elegance of proofs, I strive to make geometry accessible and engaging for learners of all levels. Let's embark on a journey of geometric discovery together!
Questions
Points A and B are at #(2 ,9 )# and #(7 ,5 )#, 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?
Two similar polygons have the scale factor 5:2. The area of the larger polygon is 100. Find the area of the smaller polygon?
Circle A has a radius of #5 # and a center of #(2 ,6 )#. Circle B has a radius of #2 # and a center of #(4 ,3 )#. If circle B is translated by #<-3 ,1 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?
Circle A has a center at #(8 ,-4 )# and a radius of #2 #. Circle B has a center at #(4 ,3 )# and a radius of #4 #. Do the circles overlap? If not what is the smallest distance between them?
A right triangle has sides A, B, and C. Side A is the hypotenuse and side B is also a side of a rectangle. Sides A, C, and the side of the rectangle adjacent to side B have lengths of #8 #, #2 #, and #14 #, respectively. What is the rectangle's area?
A solid consists of a cone on top of a cylinder with a radius equal to that of the cone. The height of the cone is #18 # and the height of the cylinder is #21 #. If the volume of the solid is #420 pi#, what is the area of the base of the cylinder?
Points A and B are at #(4 ,1 )# and #(5 ,9 )#, respectively. Point A is rotated counterclockwise about the origin by #(3pi)/2 # and dilated about point C by a factor of #4 #. If point A is now at point B, what are the coordinates of point C?
What is a 30-60-90 triangle? Please give an example.
Two corners of a triangle have angles of # (2 pi )/ 3 # and # ( pi ) / 4 #. If one side of the triangle has a length of # 19 #, what is the longest possible perimeter of the triangle?
A solid consists of a cone on top of a cylinder with a radius equal to the cone. The height of the cone is #3 # and the height of the cylinder is #12 #. If the volume of the solid is #24 pi#, what is the area of the base of cylinder?
How do you write the degree measure over 360 to find the fraction of the circle given #45^circ#?
The circumference of a circle is #88pi# #cm#. What is the radius, and the length of an arc that is 40°?
A triangle has corners at points A, B, and C. Side AB has a length of #36 #. The distance between the intersection of point A's angle bisector with side BC and point B is #14 #. If side AC has a length of #36 #, what is the length of side BC?
An ellipsoid has radii with lengths of #3 #, #3 #, and #8 #. A portion the size of a hemisphere with a radius of #2 # is removed form the ellipsoid. What is the volume of the remaining ellipsoid?
Point A is at #(-1 ,-5 )# and point B is at #(-2 ,4 )#. Point A is rotated #pi/2 # 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?
The base of a triangular pyramid is a triangle with corners at #(6 ,2 )#, #(5 ,1 )#, and #(7 ,4 )#. If the pyramid has a height of #12 #, what is the pyramid's volume?
A parallelogram has sides of length 36.4 centimeters and 21.5 centimeters. The lesser diagonal is 38.9 centimeters long. What are the interior angles of the parallelogram?
A triangle has corners at #(9 ,1 )#, #(6 ,7 )#, and #(3 ,2 )#. How far is the triangle's centroid from the origin?
What are the differences between similar triangles and congruent triangles?
Can we say that all regular polygons are made from congruent isosceles triangles?