1. By Danny Nguyen and Jimmy Nguyen

2.  Graph solids in space.  Use the Distance and Midpoint Formulas for points in space.

3.  In the coordinate plane we used an ordered pair with 2 real numbers to determine a point (x,y)  In space, we need 3 real numbers to graph a point. This is because space has 3 dimensions. These numbers make up an ordered triple (x,y,z).

4.  In space, the x-, y-, and z- axes are perpendicular to each other.  X represents the depth  Y represents the width  Z represents the height  Notice how P(2,3,6) is graphed. + _ + + _ _

5.  Graph a rectangular solid that contains point A(-4,2,4) and the origin as vertices.

6.  Plot the x-coordinate first. Go 4 units in the negative direction.  Next, plot the y- coordinate. Go 2 units in the positive direction.  Finally, plot the z- coordinate. 4 units in the positive direction  We have now plotted coordinate A.  Draw the rest of the rectangular prism.

7.  Remember Distance Formula from the coordinate plane? We also have a formula for distance in Space.

9.  Find the Distance between T(6, 0, 0) and Q(-2, 4, 2).

10.  Find the distance between A(3, 1, 4) and B(8, 2, 5) AB ( ) + ( ) + ( ) OR 33 Answer: √27

11.  We also have a formula for Midpoints in Space.

12.  An average is defined as the middle measure of a data set.  When we use midpoint formula, we are basically finding the average between the x, y, and z, coordinates.  Putting the averages together to make an ordered triple lets us find where the midpoint of the segment is in space.

13.  Determine the coordinates of the midpoint M of. T(6, 0, 0) and Q(-2, 4, 2)

14.  Find the coordinates of the midpoint M of AB. A(3, 1, 4) and B(8, 2, 5) = (,, ) Answer: (Secant), just kidding :P it is (11/2, 3/2, 9/2) or (5.5, 1.5, 4.5)

15.  Remember Translations? You can also do translations in space with solids.  It is basically the same principal we saw in Ch. 9 except we have another coordinate to translate.

16.  Find the coordinates of the vertices of the solid after the following translation. (x, y, z+20)

18.  We should also remember what a dilation is from Ch. 9. We used a matrix to find the coordinates of an image after a dilation. We can also do the same thing here.

19.  Dilate the prism to the right by a scale factor of 2. Graph the image after the dilation.

20.  First, write a vertex matrix for the rectangular prism.  Next, multiply each element of the vertex by the scale factor of 2.

21.  We now have the vertices of the dilated image.  To the right we have a graph of the dilated image.

22.  Your homework:  Pre-AP Geometry: Pg 717 #11, 12, 14, 15-26, 28, 30  Have fun doing 16 problems!