Question

1) A triangle has vertices P(–1, –5), Q(4, –11), and R(10,
–6).

Determine what type of triangle ▵PQR is.

2)A quadrilateral has vertices A(7, –2), B(9, 1), C(12, –1),
and D(10, –4).

Show that the diagonals of quadrilateral ABCD are
perpendicular to each other.

Answer #1

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Find the lengths of the sides of the triangle PQR. (a) P(4, −1,
−3), Q(8, 1, 1), R(2, 3, 1)
|PQ| =
|QR| =
|RP| =
(b)
P(5, 1, −1), Q(7, 3,
0), R(7, −3, 3)
|PQ|
=
|QR|
=
|RP|
=

Let p = (8, 10, 3, 11, 4, 0, 5, 1, 6, 2, 7, 9) and let q = (2,
4, 9, 5, 10, 6, 11, 7, 0, 8, 1, 3) be tone rows. Verify that p =
Tk(R(I(q))) for some k, and find this value of k.

Find the area of the triangle PQR when P = (-1, 3, 1), Q = (0,
5, 2), R = (4, 3, -1).

Find the area of the parallelogram PQRS with vertices P(1, 1,
0), Q(7, 1, 0), R(9, 4, 2), and S(3, 4, 2).

The vertices of a quadrilateral are listed below. A = (2, −3, 1)
B = (6, 5, −1) C = (7, 2, 2) D = (3, −6, 4) (a) Show that the
quadrilateral is a parallelogram. (b) Find the area of the
parallelogram.

5. (9 pts) Find the area of the triangle with vertices at (1,
2), (5, 7), and (3, 3) u = 〈4, 5, 0〉 and v = 〈2, 1, 0〉

1) Let a = 〈4,−5,−2〉 and b = 〈2,−4,−5〉 Find the projection of b
onto a. proj a b=
2) Find the area of a triangle PQR, where P=(−2,−4,0),
Q=(1,2,−1), and R=(−3,−6,5)
3) Complete the parametric equations of the line through the
points (7,6,-1) and (-4,4,8)
x(t)=7−11
y(t)=
z(t)=

Q
P
TR
MR
TC
MC
0
10
----
4
1
9
8
2
8
11
3
7
13
4
6
14
5
5
16
6
4
19
7
3
24
8
2
30
What profit should this firm be earning?

Show that the quadrilateral, with vertices at A(2, 0, 5), B(0,
-3, 1), C(4, 1, -2) and D(6, 4, 2), is a parallelogram. Calculate
the area. Determine the measures of the interior angles. Is the
parallelogram a rectangle? Verify your response.

10.-Construct a connected bipartite graph that is not a tree
with vertices Q,R,S,T,U,V,W.
What is the edge set?
Construct a bipartite graph with vertices Q,R,S,T,U,V,W such
that the degree of S is 4.
What is the edge set?
12.-Construct a simple graph with vertices F,G,H,I,J that has an
Euler trail, the degree of F is 1 and the degree of G is 3.
What is the edge set?
13.-Construct a simple graph with vertices L,M,N,O,P,Q that has
an Euler circuit...

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