QP=24 cm
RS=11.25 cm
QS=18.75 cm
<u>Explanation</u>:
Given that TQ bisects <RTP
(1)
consider ΔRQS and ΔRPT
QS||PT,RP and RT are transversals
(alternate angles)(2)
comparing (1) and (2)
and triangle SQT is isocelus
Therefore SQ=ST(sides opposite to equal angles in an isocelus triangle)
Therefore <RQS=<RPT(corresponding angles)
<RSQ=<RTP(corresponding angles)
therefore by AA criterion for similarity
ΔRQS~ΔRPT
According to the property of similar triangles
For this case we have the following vertices:
A (-1,1) --------> A '(3, -1)
B (-2.1)
C (-1,4)
We note that the translation rule is:
(x, y) -----------> (x + 4, y-2)
Applying the translacion rule we have:
B (-2, 1) -----------> (-2 + 4, 1-2) ------> B '(2, -1)
C (-1, 4) -----------> (-1 + 4, 4-2) ------> C '(3, 2)
Answer:
The image of vertex B or the image of Vertex C are:
B '(2, -1)
C '(3, 2)
ANSWER
8, 10, 12, 14, . . .
EXPLANATION
The given rule for the sequence is :
f(n)=2n+6
The domain for a sequence is the set of natural numbers.
When n=1,
f(1)=2(1)+6=8
When n=2,
f(2)=2(2)+6=10
When n=3,
f(3)=2(3)+6=12
When n=4,
f(4)=2(4)+6=14
Therefore the sequence that follows the given rule is
8, 10, 12, 14, . . .
Answer:
Reason:
1) assumptions given
2) RUTS is a rectangle
3) RUTS is a rectangle
4) because:
+) ∠STU and ∠SRU are the right angles
+) RU = ST; UT = RS
=> ΔURS ≅ ΔSTU (SAS)
5) because ΔURS ≅ ΔSTU (SAS) => ∠USR = ∠SUT
Step-by-step explanation:
