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?