Ella Armstrong
Geometry teacher | Tutor for 7 years
I'm a passionate educator specializing in geometry. My journey began at Beloit College, where I delved deep into the intricacies of shapes, angles, and spatial relationships. With a keen eye for detail and a love for problem-solving, I aim to make geometry not just understandable but enjoyable for my students. Whether it's exploring the beauty of proofs or unraveling the mysteries of three-dimensional figures, I'm dedicated to fostering a supportive learning environment where students can thrive and develop their mathematical skills to their fullest potential.
Questions
Can we say that all regular polygons are made from congruent isosceles triangles?
Points A and B are at #(4 ,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 corners of a triangle have angles of # ( pi )/ 3 # and # ( pi ) / 4 #. If one side of the triangle has a length of # 9 #, what is the longest possible perimeter of the triangle?
Circle A has a center at #(2 ,9 )# and an area of #16 pi#. Circle B has a center at #(3 ,8 )# and an area of #67 pi#. Do the circles overlap?
A line passes through #(9 ,3 )# and #( 3, 5 )#. A second line passes through #( 7, 8 )#. What is one other point that the second line may pass through if it is parallel to the first line?
Points #(2 ,9 )# and #(1 ,5 )# are #(3 pi)/4 # radians apart on a circle. What is the shortest arc length between the points?
A triangle has corners at points A, B, and C. Side AB has a length of #24 #. The distance between the intersection of point A's angle bisector with side BC and point B is #9 #. If side AC has a length of #35 #, what is the length of side BC?
What is the area of an equilateral triangle with a side length of 1?
A circle has a chord that goes from #( 4 pi)/3 # to #(17 pi) / 12 # radians on the circle. If the area of the circle is #27 pi #, what is the length of the chord?
A triangle has vertices A, B, and C. Vertex A has an angle of #pi/12 #, vertex B has an angle of #(pi)/2 #, and the triangle's area is #2 #. What is the area of the triangle's incircle?
Given two similar triangles with a scale factor of a : b, show the ratio of their perimeters is also a : b?
A rectangle with sides 7 and #x+2# has a perimeter of 40 units. What is the value of #x#?
A triangle has corners at #(-5 ,6 )#, #(2 ,-3 )#, and #(8 ,9 )#. If the triangle is dilated by a factor of #5 # about point #(-3 ,6 ), how far will its centroid move?
A line segment has endpoints at #(2 ,1 )# and #(6 ,2 )#. The line segment is dilated by a factor of #4 # around #(2 ,1 )#. What are the new endpoints and length of the line segment?
Two circles have the following equations #(x -1 )^2+(y -4 )^2= 64 # and #(x +3 )^2+(y +1 )^2= 9 #. 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?
A square and a equilateral triangle are to be formed out of the same piece of wire. The wire is 6 inches long. What is the maximum of the total area the square and the triangle?
A rectangle has a perimeter of 48 ft. The length and width are scaled by a factor 1.5. What is the perimeter of the resulting rectangle?
What is the perimeter of a triangle with corners at #(7 ,5 )#, #(1 ,2 )#, and #(4 ,8 )#?
Triangle ABC is graphed on a coordinate plane. find the length of AB?
A circle has a center that falls on the line #y = 7/9x +7 # and passes through # ( 4 ,5 )# and #(8 ,7 )#. What is the equation of the circle?