GSE Geometry Date: ________________________ Volume of a Prism Choose odd or even number questions in each row. Rectangular Prism ...

GSE Geometry Date: ________________________

Volume of a Prism

Choose odd or even number questions in each row.

GSE Geometry Date: ________________________

Volume of a Pyramid

Find the volume of the pyramids unless stated. You must choose two word problems.

GSE Geometry Name______________________

Midpoint Formula

Ratio of partition is 1:1 because line is split right down the middle

Steps to find coordinate of midpoint: Example 1: Given two endpoints of a segment, find the Midpoint

1. Label x₁, y₁, x₂, and y₂
   of the segment (-5, 8) and (4, -2)


2. Plug values into formula


3. Calculate each part separately


4. State your answer as an ordered pair (x, y)

Steps to find coordinate of endpoint Example 2: Find point B so that point M is the
midpoint
of segment

1. Label x₁, y₁, x₂, and y₂
   AB. A(-2, 6), B(x , y) and Midpoint = (2, 2)


2. Plug values into formula


3. Write out each part separately


4. Solve for x in the 1st equation and

y in the 2nd equation

Find the midpoint of the line segment with the given endpoints.

1) (5, 9), (-1, 9) 2) (8, -9), (0, 5) 3) (-4, 2), (2, -3) 4) (2, -11), (-9, 0)

5) Find the coordinates of point F (x, y) such that B is (3, 5) and the midpoint of BF is (-4, 6)

GSE Geometry Name______________________

Notes on Partitioning a Segment in Two Dimensions

Example: Find the coordinates of P along the directed line segment AB so that the ratio of AP to PB is 3 to 2.

Using the above formula, substituting we get

(x,y) =

1. Find the coordinates of point P along the directed line segment AB so that AP to PB is the given ratio.

A(1, 3), B(8, 4); 4 to 1. 70 + 23 =

Here a:b = 4:1

Using the above formula if P has coordinates (x,y) then

(x,y) =( =(33/5, 19/5) = (6.6,3.8)

2. Find the coordinates of point P along the directed line segment AB so that AP to PB is the given ratio.

A(8, 0), B(3, -2); 1 to 4. equal for 20 - 20 =

Here a:b = 1:4

Using formula coordinates of P

= (x,y) =

GSE Geometry Name: ______________________________

Cross sections of 3D shapes/Volumes of Revolution

1.
What would the cross section of the following diagram be?

2.
What would the cross section of the following diagram be?

3.

4.

5.

6.
What three dimensional shape will be created by rotating the circle about the given line in the diagram.

(a) Cylinder (b) Cone (c) Circular Prism (d) Sphere

7.
What three dimensional shape will be created by rotating the square about the given line in the diagram.

(a) Cylinder (b) Square Prism (c) Rectangular Prism (d) Cone

8 – 12: Choose the correct name for each 3-D figure.

8. 9. 10.

11. 12.