CC Geometry H
Aim #6: How do we determine the perpendicularity of any two segments in the
coordinate plane?
Do Now:
1. Are the segments through the origin and the points A(9,10) and B(10,9)
perpendicular? Justify using the perpendicularity criterion.
2. Given points O(0,0), A(4,3) and B(6,-8), determine if
OA OB using two methods.
O
3. Given points O(0,0), A(3,-2) and B(-4, y), find y so that OA
OB.
Given M(5,2), N(1,-4), and L(-1,6), determine if LM and MN are perpendicular using
two methods.
Are the lines containing segments perpendicular?
Example: Given A(2,2), B(10,16), C(-3,1) and D(4,-3), is AB
two methods.
CD? Determine using
B
A
C
D
Given points A(a1,a2), B(b1,b2), C(c1,c2), and D(d1,d2), can you find a formula, in
terms of the coordinates, that will allow us to determine whether segments AB
and CD are perpendicular?
Is AB
CD if A(3,2), B(7,10), C(-2,-3), and D(4,-6)? Use two methods.
A robot is traveling along a linear path with equation y = 3x - 600. The robot
hears a "ping" from a tracking device when it reaches B(400,600), and turns to
travel along a linear path with equation y - 600 =
.
y
B(400,600)
C
A
x
­600
a. If point A is the y-intercept of the original equation, what are the coordinates of
point A?
b. What are the endpoints of the original segment of motion?
c. If the beacon lies on the x-axis at point C, what is the y-value of this point?
d. Translate B to the origin. State the coordinates of A'(
B'(0, 0), and C'(
,
).
,
)
e. Use the perpendicularity criterion to determine the coordinates of point C.
Let's Sum It Up!
-Translating segments that are perpendicular does not change their
perpendicularity or angle measure. A translation is a rigid motion.
Name______________________
Date ________________
CC Geometry H
HW #6
1. Given points S(2,4), T(7,6), U(-3,-4), and B(-1,-9)
a. Translate segments ST and UV so that the image
of each segment has an endpoint at the origin.
b. Are the segments perpendicular?
(Use the perpendicularity criterion.)
c. Are the lines ST and UV perpendicular? Explain.
T(7,6)
S(2,4)
U(­3,­4)
V(­1,­9)
2. Given M(5,2), N(1,-4), and L listed below, determine if LM and MN are
perpendicular.
a. L(11,-2)
b. L(1,4)
3. Is GH
IJ if G(-4,1), H(3,2), I(-2,-3), and J(-3,4)? Justify your answer.
4. Determine the missing vertex of a right triangle with vertices R(6,2) and
S(5,5) if the third vertex, T, is on the y-axis.
a. Represent point T: ( , )
b. Translate S to the origin.
c. State the coordinates of the translated vertices:
(
,
)
S'(0,0)
T'(
,
)
d. Apply the perpendicularity criterion
to solve for the missing coordinate.
e. Verify your answer by comparing slopes.
Review
True or false?
1.
1. Planes W and X intersect at KL.
W
2. Points K, L, M, and N are coplanar.
M
Q
J
R
3. Points Q, J, and M are collinear.
K
N
L
X
P
4. MN and RP intersect.
5. JK lies in plane X.
6. ≮PLK is a right angle.
7. ≮NKL and ≮JKM are vertical angles.
8. ≮NKJ and ≮JKM are supplementary angles.
2. Are the segments through the origin and the points A(9,6) and B(4,-6)
perpendicular? Justify.