# Evelyn Arboleda

Geometry teacher | Verified Expert

I hold a degree in Geometry from Dakota State University. My passion lies in unraveling the intricacies of shapes and space, guiding students through the wonders of geometric concepts. With a knack for simplifying complex ideas, I foster a supportive learning environment where students thrive. Whether exploring angles, polygons, or proofs, I'm dedicated to illuminating the beauty and logic of Geometry. Let's embark on this geometric journey together!

## Questions

A triangle has corners at #(2 ,-5 )#, #(-1 ,2 )#, and #(3 ,-3 )#. If the triangle is dilated by a factor of #2/5 # about point #(-1 ,3 ), how far will its centroid move?

A line passes through #(6 ,2 )# and #(5 ,7 )#. A second line passes through #(1 ,7 )#. What is one other point that the second line may pass through if it is parallel to the first line?

A pyramid has a base in the shape of a rhombus and a peak directly above the base's center. The pyramid's height is #9 #, its base's sides have lengths of #4 #, and its base has a corner with an angle of #( pi)/6 #. What is the pyramid's surface area?

Verify that the Euler's formula is correct?

A triangle has two corners with angles of # (3 pi ) / 4 # and # ( pi )/ 8 #. If one side of the triangle has a length of #7 #, what is the largest possible area of the triangle?

A line segment has endpoints at #(8 ,2 )# and #(2 ,3 )#. If the line segment is rotated about the origin by # pi #, translated horizontally by # - 1 #, and reflected about the y-axis, what will the line segment's new endpoints be?

Delroy’s sailboat has two sails that are similar triangles. The larger sail has sides of 10 feet, 24 feet, and 26 feet. If the shortest side of the smaller sail measures 6 feet, what is the perimeter of the smaller sail?

Circle A has a radius of #5 # and a center of #(2 ,7 )#. Circle B has a radius of #1 # and a center of #(3 ,1 )#. If circle B is translated by #<1 ,3 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?

A triangle has sides with lengths of 4, 9, and 8. What is the radius of the triangles inscribed circle?

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 #6 #. If the volume of the solid is #320 pi#, what is the area of the base of the cylinder?

A triangle has corners A, B, and C located at #(2 ,7 )#, #(5 ,3 )#, and #(9 , 4 )#, respectively. What are the endpoints and length of the altitude going through corner C?

A triangle has corners A, B, and C located at #(2 ,2 )#, #(3 ,4 )#, and #(6 ,1 )#, respectively. What are the endpoints and length of the altitude going through corner C?

Circle A has a radius of #2 # and a center at #(8 ,3 )#. Circle B has a radius of #3 # and a center at #(3 ,5 )#. If circle B is translated by #<-2 ,4 >#, does it overlap circle A? If not, what is the minimum distance between points on both circles?

A pyramid has a base in the shape of a rhombus and a peak directly above the base's center. The pyramid's height is #5 #, its base has sides of length #7 #, and its base has a corner with an angle of #(2 pi)/3 #. What is the pyramid's surface area?

Yosief is 4 feet 9 inch boy. He stands in front of a tree and sees that it's shadow coincide with his. Yosief shadow measures 9 feet 6 inches. Yosief measures the distance between him and the tree to calculate its height, how does he do it?

How do you find the surface area of the sphere in terms #pi# given #S=4pir^2# and r= 1.2 ft?

Cups A and B are cone shaped and have heights of #22 cm# and #25 cm# and openings with radii of #6 cm# and #11 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?

A line segment has endpoints at #(9 ,6 )# and #(5 ,3)#. If the line segment is rotated about the origin by #pi #, translated vertically by #2 #, and reflected about the x-axis, what will the line segment's new endpoints be?

How would I solve #cos x + cos 2x = 0#? Please show steps.

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