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
A line segment has endpoints at #(7 ,4 )# and #(8 ,5 )#. If the line segment is rotated about the origin by #(3 pi)/2 #, translated vertically by #-2 #, and reflected about the y-axis, what will the line segment's new endpoints be?
Points #(2 ,5 )# and #(3 ,4 )# are #( pi)/3 # radians apart on a circle. What is the shortest arc length between the points?
Two circles have the following equations: #(x +3 )^2+(y -1 )^2= 64 # and #(x -7 )^2+(y +2 )^2= 25 #. 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?
Triangle A has sides of lengths #60 #, #42 #, and #60 #. Triangle B is similar to triangle A and has a side of length #7 #. What are the possible lengths of the other two sides of triangle B?
How many sides are in a polygon whose sum of the interior angles is 1440?
Two opposite sides of a parallelogram each have a length of #6 #. If one corner of the parallelogram has an angle of #(3pi)/8 # and the parallelogram's area is #48 #, how long are the other two sides?
Two corners of an isosceles triangle are at #(8 ,6 )# and #(7 ,5 )#. If the triangle's area is #64 #, what are the lengths of the triangle's sides?
A circle has a center that falls on the line #y = 3/8x +8 # and passes through # ( 7 ,4 )# and #(2 ,9 )#. What is the equation of the circle?
Two corners of a triangle have angles of # (5 pi )/ 12 # and # ( pi ) / 3 #. If one side of the triangle has a length of # 1 #, what is the longest possible perimeter of the triangle?
A triangle has two corners with angles of # ( pi ) / 3 # and # ( pi )/ 6 #. If one side of the triangle has a length of #18 #, what is the largest possible area of the triangle?
A line segment has endpoints at #(3 , 4)# and #(2 , 6)#. If the line segment is rotated about the origin by #(3pi)/2 #, translated horizontally by #-2#, and reflected about the y-axis, what will the line segment's new endpoints be?
The base of a triangular pyramid is a triangle with corners at #(7 ,6 )#, #(4 ,3 )#, and #(1 ,5 )#. If the pyramid has a height of #6 #, what is the pyramid's volume?
A triangle has vertices A, B, and C. Vertex A has an angle of #pi/12 #, vertex B has an angle of #pi/8 #, and the triangle's area is #14 #. What is the area of the triangle's incircle?
Point A is at #(4 ,-8 )# and point B is at #(-1 ,-2 )#. Point A is rotated #(3pi)/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?
Triangle A has sides of lengths #27 #, #12 #, and #21 #. Triangle B is similar to triangle A and has a side of length #3 #. What are the possible lengths of the other two sides of triangle B?
Circle A has a center at #(5 ,4 )# and a radius of #3 #. Circle B has a center at #(6 ,-8 )# and a radius of #1 #. Do the circles overlap? If not, what is the smallest distance between them?
A triangle has corners at #(7 ,4 )#, #(4 ,6 )#, and #(6 ,7 )#. What is the area of the triangle's circumscribed circle?
A triangle has corners A, B, and C located at #(6 ,4 )#, #(2 ,5 )#, and #(3 , 1 )#, respectively. What are the endpoints and length of the altitude going through corner C?
A triangle has corners at #(4 ,-6 )#, #(3 ,-3 )#, and #(8 ,4 )#. If the triangle is dilated by a factor of #1/3 # about point #(-3 ,2 ), how far will its centroid move?
Triangle A has sides of lengths #2 ,3 #, and #9 #. Triangle B is similar to triangle A and has a side of length #1 #. What are the possible lengths of the other two sides of triangle B?