# Aurora Ayala

Geometry teacher | Verified Expert

With a passion for Geometry ignited during my undergraduate years, I pursued my major in this field, delving deep into its intricate concepts and applications. After graduation, I embarked on a unique journey, attending Brooklyn Law School to broaden my horizons and gain diverse perspectives. Combining my expertise in Geometry with legal acumen, I offer comprehensive guidance and insights to students navigating the complexities of mathematics. My interdisciplinary approach fosters critical thinking and problem-solving skills, empowering learners to excel academically and beyond. Join me in unraveling the wonders of Geometry and unlocking your full potential.

## Questions

A line segment is bisected by a line with the equation # - 3 y + 6 x = 5 #. If one end of the line segment is at #( 3 , 3 )#, where is the other end?

A circle has a center that falls on the line #y = 1/7x +4 # and passes through # ( 7 ,8 )# and #(3 ,6 )#. What is the equation of the circle?

The base of a triangular pyramid is a triangle with corners at #(2 ,2 )#, #(3 ,1 )#, and #(7 ,3 )#. If the pyramid has a height of #6 #, what is the pyramid's volume?

Point A is at #(5 ,-2 )# and point B is at #(-2 ,5 )#. Point A is rotated #pi/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?

Cups A and B are cone shaped and have heights of #35 cm# and #23 cm# and openings with radii of #14 cm# and #9 cm#, respectively. If cup B is full and its contents are poured into cup A, will cup A overflow? If not how high will cup A be filled?

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

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 #18 # and the height of the cylinder is #1 #. If the volume of the solid is #21 pi#, what is the area of the base of the cylinder?

What is the orthocenter of a triangle with corners at #(9 ,7 )#, #(4 ,4 )#, and (8 ,6 )#?

Circle A has a center at #(2 ,3 )# and an area of #8 pi#. Circle B has a center at #(7 ,2 )# and an area of #64 pi#. Do the circles overlap?

A triangle has corners at points A, B, and C. Side AB has a length of #42 #. 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 #45 #, what is the length of side BC?

And I saucily‘s right triangles legs are 10 square root of 8 feet long. What is the length of the hypotenuse?

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 #42 # and the height of the cylinder is #10 #. If the volume of the solid is #144 pi#, what is the area of the base of the cylinder?

A parallelogram has sides A, B, C, and D. Sides A and B have a length of #2 # and sides C and D have a length of # 1 #. If the angle between sides A and C is #(7 pi)/18 #, what is the area of the parallelogram?

Circle A has a center at #(3 ,7 )# and an area of #56 pi#. Circle B has a center at #(9 ,6 )# and an area of #28 pi#. Do the circles overlap?

Triangle ABC is graphed on a coordinate plane. find the length of AB?

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?

Two corners of a triangle have angles of # (5 pi )/ 8 # and # ( pi ) / 4 #. If one side of the triangle has a length of # 7 #, what is the longest possible perimeter of the triangle?

Two opposite sides of a parallelogram each have a length of #16 #. 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?

Angles A and B are corresponding angles formed by two parallel lines cut by a transversal. If #m/_A = 4x# and #m/_B = 3x+7#, what is the value of #x#?

Triangle A has an area of #3 # and two sides of lengths #5 # and #6 #. Triangle B is similar to triangle A and has a side with a length of #11 #. What are the maximum and minimum possible areas of triangle B?