# Caroline Aucoin

Geometry teacher | Verified Expert

I hold a degree in Geometry from Montclair State University. With a passion for unlocking the mysteries of shapes and spaces, I guide students through the intricacies of geometric concepts. My teaching style emphasizes clarity and practical application, empowering learners to excel in problem-solving and critical thinking. Drawing on my academic background and real-world experience, I foster a supportive learning environment where curiosity thrives. Together, we'll explore the fascinating world of geometry and uncover its relevance in everyday life. Let's embark on this journey of discovery together.

## Questions

A triangle has corners at #(-3 ,-1 )#, #(5 ,6 )#, and #(-4 ,7 )#. If the triangle is dilated by a factor of #1/3 # about point #(2 ,-1 ), how far will its centroid move?

Two corners of an isosceles triangle are at #(3 ,9 )# and #(2 ,7 )#. If the triangle's area is #4 #, what are the lengths of the triangle's sides?

Two opposite sides of a parallelogram each have a length of #24 #. If one corner of the parallelogram has an angle of #(11 pi)/12 # and the parallelogram's area is #72 #, how long are the other two sides?

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

A chord with a length of #6 # runs from #pi/8 # to #pi/6 # radians on a circle. What is the area of the circle?

A triangle has corners at #(9 ,3 )#, #(4 ,1 )#, and #(2 ,8 )#. What is the area of the triangle's circumscribed circle?

Quadrilateral PQRS is a parallelogram such that its diagonals PR = QS = 8 cm, measure of angle PSR = 90 degrees, measure of angle QSR = 30 degrees. What is the perimeter of quadrilateral PQRS?

How much metal is needed to cast a cubical metal box with outer side 10 inches long if the thickness of its walls should be exactly 2 inches?

Two corners of an isosceles triangle are at #(2 ,4 )# and #(3 ,8 )#. If the triangle's area is #64 #, what are the lengths of the triangle's sides?

What is the area of a rhombus?

Write the equation of a circle with a radius of 10 and a center of (-2,5)?

A line segment has endpoints at #(1 ,2 )# and #(3 ,4 )#. The line segment is dilated by a factor of #6 # around #(2 ,5 )#. What are the new endpoints and length of the line segment?

A parallelogram has sides with lengths of #12 # and #6 #. If the parallelogram's area is #42 #, what is the length of its longest diagonal?

Two corners of an isosceles triangle are at #(7 ,6 )# and #(4 ,9 )#. If the triangle's area is #24 #, what are the lengths of the triangle's sides?

Two corners of a triangle have angles of # (5 pi )/ 8 # and # ( pi ) / 12 #. If one side of the triangle has a length of # 8 #, what is the longest possible perimeter of the triangle?

A line passes through #(3 ,9 )# and #(6 ,8 )#. A second line passes through #(7 ,6 )#. What is one other point that the second line may pass through if it is parallel to the first line?

The base of a triangular pyramid is a triangle with corners at #(7 ,6 )#, #(4 ,2 )#, and #(3 ,8 )#. If the pyramid has a height of #6 #, what is the pyramid's volume?

In an isosceles trapezoid ABCD, AB=CD=5. The top base = 8 and the bottom base = 14. What is the area of this trapezoid?

A triangle has corners at points A, B, and C. Side AB has a length of #27 #. The distance between the intersection of point A's angle bisector with side BC and point B is #15 #. If side AC has a length of #36 #, what is the length of side BC?

A line passes through #(2 ,4 )# and #(7 ,3 )#. A second line passes through #(8 ,5 )#. What is one other point that the second line may pass through if it is parallel to the first line?