# Sadie Adams

Geometry teacher | Verified Expert

Greetings! I'm a dedicated geometry expert, honing my skills at Loyola University Maryland. Passionate about shaping mathematical minds, I thrive on unraveling the complexities of geometry. With a commitment to fostering understanding, I'm here to guide students through the intricacies of shapes, angles, and the beauty of mathematical relationships. Let's embark on a journey of geometric exploration together!

## Questions

A triangle has corners at #(6 ,6 )#, #(7 ,4 )#, and #(1 ,2 )#. How far is the triangle's centroid from the origin?

A line segment has endpoints at #(2 ,6 )# and #(7 , 3 )#. If the line segment is rotated about the origin by # pi /2 #, translated horizontally by # 1 #, and reflected about the x-axis, what will the line segment's new endpoints be?

What is the perimeter of a triangle with corners at #(7 ,9 )#, #(8, 2 )#, and #(9 ,2 )#?

A pyramid has a parallelogram shaped base and a peak directly above its center. Its base's sides have lengths of #7 # and #4 # and the pyramid's height is #6 #. If one of the base's corners has an angle of #pi/3#, what is the pyramid's surface area?

The figure shows △ABC.¯¯BD¯ is the angle bisector of ∠ABC. What is AD ?

What is the orthocenter of a triangle with corners at #(5 ,7 )#, #(2 ,3 )#, and (4 ,5 )#?

The base of a triangular pyramid is a triangle with corners at #(6 ,2 )#, #(3 ,5 )#, and #(4 ,2 )#. If the pyramid has a height of #8 #, what is the pyramid's volume?

A parallelogram has sides with lengths of #21 # and #12 #. If the parallelogram's area is #84 #, what is the length of its longest diagonal?

What is the centroid of a triangle with corners at #(9 , 2 )#, #(4 , 6 )#, and #(5 , 8 )#?

A triangle has corners at #(5 ,7 )#, #(2 ,1 )#, and #(3 ,6 )#. What is the area of the triangle's circumscribed circle?

A triangle has corners A, B, and C located at #(2 ,7 )#, #(7 ,5 )#, and #(3 , 2 )#, respectively. What are the endpoints and length of the altitude going through corner C?

If the length of a rectangle is represented by #(5x-3)# and the width is represented by #(2x)#, what is the area of the rectangle in terms of #x#? Please show working.

A solid consists of a cone on top of a cylinder with a radius equal to the cone. The height of the cone is #3 # and the height of the cylinder is #12 #. If the volume of the solid is #24 pi#, what is the area of the base of cylinder?

A triangle has corners at #(9 ,4 )#, #(2 ,6 )#, and #(5 ,8 )#. How far is the triangle's centroid from the origin?

What is the area of a parallelogram with corners at these coordinates on a plane: (-2,-1), (-12,-4), (9,-4), (-1,-7)?

What is the equation of the circle with a center at #(3 ,5 )# and a radius of #1 #?

A triangle has corners A, B, and C located at #(6 ,8 )#, #(7 ,4 )#, and #(5 ,3 )#, respectively. What are the endpoints and length of the altitude going through corner C?

How do you use Heron's formula to find the area of a triangle with sides of lengths #8 #, #3 #, and #9 #?

Triangle A has an area of #9 # and two sides of lengths #3 # and #9 #. Triangle B is similar to triangle A and has a side with a length of #7 #. What are the maximum and minimum possible areas of triangle B?

How many acute angles can an isosceles triangle have?