# Noah Atkinson

Geometry teacher | Tutor for 8 years

I am a dedicated educator specializing in Geometry, with a background in Mathematics from Washington and Lee University. My passion lies in guiding students through the intricate world of shapes, angles, and proofs, fostering their understanding and appreciation for the subject. With a commitment to clarity and patience, I strive to make geometric concepts accessible and engaging for learners of all levels. Through personalized instruction and effective problem-solving strategies, I aim to empower students to excel in their mathematical journey. Let's unlock the mysteries of Geometry together!

## Questions

If #P(x,y)# lies on the interval #A(x_1,y_1), B(x_2,y_2)# such that #AP : PB =a : b#, with a and b positive, show that #x= (bx_1+ax_2) /(b+a)# and #y=(by_1+ay_2)/(b+a)#?

An isosceles triangle has sides A, B, and C, such that sides A and B have the same length. Side C has a length of #16 # and the triangle has an area of #108 #. What are the lengths of sides A and B?

I need an expression in simplest form for the perimeter of a triangle, left side of the triangle says 2x bottom line says 4x-2 and right side says 2x+3?

A circle's center is at #(8 ,3 )# and it passes through #(2 ,5 )#. What is the length of an arc covering #( pi ) /6 # radians on the circle?

How does a vertical translation change the x- and y-coordinates of the endpoints of each side of an angle?

An ellipsoid has radii with lengths of #8 #, #9 #, and #5 #. A portion the size of a hemisphere with a radius of #5 # is removed form the ellipsoid. What is the volume of the remaining ellipsoid?

What is a 4 sided polygon?

What is the equation of the circle with a center at #(4 ,-7 )# and a radius of #4 #?

Triangle A has sides of lengths #48 ,24 #, and #54 #. Triangle B is similar to triangle A and has a side of length #5 #. What are the possible lengths of the other two sides of triangle B?

A cylindrical barrel has a radius of 7.6 ft and a height of 11.8 ft. Tripling what dimension(s) will triple the volume of the barrel?

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

A triangle has corners at #(4 , 5 )#, #(1 ,3 )#, and #(5 ,3 )#. What is the radius of the triangle's inscribed circle?

Two rhombuses have sides with lengths of #15 #. If one rhombus has a corner with an angle of #(3pi)/8 # and the other has a corner with an angle of #(5pi)/6 #, what is the difference between the areas of the rhombuses?

A line segment is bisected by a line with the equation # 4 y - 6 x = 8 #. If one end of the line segment is at #( 8 , 3 )#, where is the other end?

Angles L and M are complementary. If the measurement of angle L is 16 degrees, what is the measurement of angel M?

Circle A has a center at #(1 ,3 )# and an area of #45 pi#. Circle B has a center at #(2 ,7 )# and an area of #75 pi#. Do the circles overlap?

A parallelogram has sides with lengths of #21 # and #12 #. If the parallelogram's area is #48 #, what is the length of its longest diagonal?

The area of the label is 300 cm. The height of the label is 12 cm. What is the length of the label show working?

An isosceles triangle has sides A, B, and C, such that sides A and B have the same length. Side C has a length of #32 # and the triangle has an area of #16 #. What are the lengths of sides A and B?

Is is true that a regular polygon has all sides of the same length and all internal angles the same?