Translate triangle a by vector (-3/1)to give triangle b. Then rotate your triangle b 180 degrees around the origin to give trian
gle. Describe fully the single transformation that maps triangle a onto triangle c
1 answer:
Answer:
Rotate triangle A about the point (1.5, -0.5) by 180°.
Step-by-step explanation:
Translating a figure by a vector means shifting it 3 units left along the x-axis and 1 unit up along the y-axis.
The translation rule can be expressed as:
(x, y) → [(x - 3), (y + 1)]
Based on the provided figure,
The coordinates of triangle A are A(1, -1), B(1, -4) and C(3, -4)
Post-translation, the new coordinates are A'(-2, 0), B'(-2, -3), C'(0, -3).
Next, applying a 180° rotation to these new points about the origin gives:
Rotation rule:
(x, y) → (-x, -y)
A'(-2, 0) → A"(2, 0)
B'(-2, -3) → B"(2, 3)
C'(0, -3) → C"(0, 3)
Thus, the transformation A(1, -1) → A"(2, 0) represents the entire transformation.
The rule defining the transformation mapping triangle C to A would be expressed as:
Rotate triangle A about the point (1.5, -0.5) by 180°.
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Answer: C) HF measures 4 units and GH is 2 units.
Step-by-step explanation:
The SSS similarity theorem asserts that triangles are similar if the lengths of their corresponding sides are in proportion.
For triangles ΔDFE and ΔGFH:
DG equals 15, GF is 5, EH equals 12, and DE is 8.
To demonstrate the similarity of ΔDFE and ΔGFH according to the SSS similarity theorem, we require:
Thus, to confirm that △DFE is similar to △GFH utilizing the SSS similarity theorem and the data from the diagram, it is essential to establish that HF measures 4 units and GH measures 2 units.
Answer:
4.0921 reflects the logarithm of the equilibrium constant.
Step-by-step explanation:
; E° = - 0.41 V
; E° = 0.80 V
Iron has a negative reduction potential, indicating its tendency to lose electrons and undergo oxidation, and thus it will be at the anode.
=Reduction potential of cathode - Reduction potential of anode
; E° = - 0.41 V
; E° = 0.80 V
Net reaction:
n = 2
To determine the equilibrium constant, we utilize the correlation with Gibbs free energy, as follows:
and,
Aligning these two equations yields:
where,
n = electrons transferred = 2
F = Faraday's constant = 96500 C
= standard electrode potential of the cell = 1.21 V
R = gas constant = 8.314 J/K.mol
T = reaction temperature =
Substituting values into the equation, we arrive at:
4.0921 represents the logarithm of the equilibrium constant.