# 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

Using the midpoint formula, if you're only given #((x_1 + x_2) / 2#, #(y_1 + y_2) / 2)#, is it possible to solve for #x# and #y#?

Circle A has a radius of #3 # and a center of #(2 ,7 )#. Circle B has a radius of #2 # and a center of #(6 ,1 )#. If circle B is translated by #<2 ,7 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?

Two corners of an isosceles triangle are at #(9 ,6 )# and #(4 ,7 )#. If the triangle's area is #64 #, what are the lengths of the triangle's sides?

A circle has a chord that goes from #pi/3 # to #(3 pi) / 8 # radians on the circle. If the area of the circle is #81 pi #, what is the length of the chord?

A triangle has corners A, B, and C located at #(8 ,7 )#, #(1 ,5 )#, and #(6 , 3 )#, respectively. What are the endpoints and length of the altitude going through corner C?

A triangle has corners A, B, and C located at #(4 ,2 )#, #(3 ,4 )#, and #(6 ,8 )#, respectively. What are the endpoints and length of the altitude going through corner C?

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 #9 # and the height of the cylinder is #12 #. If the volume of the solid is #45 pi#, what is the area of the base of the cylinder?

An isosceles trapezoid has one base of 12 inches and legs of 6 inches. What should its top base be in width if we wanted to maximize its area?

A triangle has corners at points A, B, and C. Side AB has a length of #15 #. The distance between the intersection of point A's angle bisector with side BC and point B is #7 #. If side AC has a length of #24 #, what is the length of side BC?

What is the orthocenter of a triangle with corners at #(2 ,6 )#, #(9 ,1 )#, and (5 ,3 )#?

A line passes through #(9 ,2 )# and #( 3, 8 )#. A second line passes through #( 4, 1 )#. What is one other point that the second line may pass through if it is parallel to the first line?

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

A triangle has corners at #(6 ,9 )#, #(-2 ,-1 )#, and #(1 ,-1 )#. If the triangle is dilated by a factor of #1/3 # about point #(-5 ,-2 ), how far will its centroid move?

A line segment is bisected by a line with the equation # 7 y + x = 7 #. If one end of the line segment is at #(1 ,3 )#, where is the other end?

What is a dilation, or scaling around a point?

A triangle has corners at #(5 , 2 )#, #(4 ,7 )#, and #(5 ,6 )#. What is the radius of the triangle's inscribed circle?

If the volume of a sphere doubles, what is the ratio of the surface area of the new, larger sphere to the old?

A circle's center is at #(7 ,2 )# and it passes through #(5 ,6 )#. What is the length of an arc covering #(7pi ) /4 # radians on the circle?

An isosceles triangle has sides A, B, and C with sides B and C being equal in length. If side A goes from #(1 ,4 )# to #(5 ,1 )# and the triangle's area is #15 #, what are the possible coordinates of the triangle's third corner?

The 2 equal sides of an isosceles triangle are 5.7 cm each. The base is 7 cm. What is the height?