Download Midpoint Formula in Space

By Danny Nguyen and Jimmy Nguyen
 Graph solids in space.
 Use the Distance and
Midpoint Formulas for points
in space.


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).
+





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.
_
_
+
+
_

Graph a rectangular solid that contains point
A(-4,2,4) and the origin as vertices.





Plot the x-coordinate
first. Go 4 units in the
negative direction.
Next, plot the ycoordinate. Go 2 units in
the positive direction.
Finally, plot the zcoordinate. 4 units in the
positive direction
We have now plotted
coordinate A.
Draw the rest of the
rectangular prism.

Remember Distance Formula from the
coordinate plane? We also have a formula for
distance in Space.

Find the Distance between T(6, 0, 0) and
Q(-2, 4, 2).

Find the distance between A(3, 1, 4) and
B(8, 2, 5)
AB
AB
(
(
) + (
) + (
) + (
) + (
Answer: √27
OR
)
)
3
3

We also have a formula for Midpoints in
Space.



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.

Determine the coordinates of the midpoint
M of
. T(6, 0, 0) and Q(-2, 4, 2)

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)


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.

Find the coordinates of
the vertices of the solid
after the following
translation. (x, y, z+20)

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.

Dilate the prism to the
right by a scale factor
of 2. Graph the image
after the dilation.
First, write a vertex
matrix for the
rectangular prism.
 Next, multiply each
element of the vertex
by the scale factor of 2.

We now have the
vertices of the dilated
image.
 To the right we have a
graph of the dilated
image.


Your homework:
 Pre-AP Geometry: Pg 717 #11, 12, 14, 15-26, 28, 30
 Have fun doing 16 problems! 