△DEF has vertices D (2,2), E (-2,-1), and F (-3,5). Complete the following charts indicating the location of △D′E′F′ and △D″E″F″
.△DEF is reflected in the y-axis. Then it is translated along the vector ⟨3,−5⟩. Enter your answers as points using parenthesis and commas. Do not use any spaces.
1 answer:
Reflecting DEF on the y-axis gives the following coordinates of D'E'F' as follows
the coordinate of D' (-2, 2)
the coordinate of E' (2, -1)
the coordinate of F' (3, 5)
Translating D'E'F' by the vector (3, -5) gives the following coordinate of D''E''F'' as follows
the coordinate of D'' (-2+3, 2-5) = (1, -3)
the coordinate of E'' (2+3, -1-5) = (5, -6)
the coordinate of F'' (3+3, 5-5) = (6, 0)
The diagram below shows the transformation of triangle DEF
the coordinate of D' (-2, 2)
the coordinate of E' (2, -1)
the coordinate of F' (3, 5)
Translating D'E'F' by the vector (3, -5) gives the following coordinate of D''E''F'' as follows
the coordinate of D'' (-2+3, 2-5) = (1, -3)
the coordinate of E'' (2+3, -1-5) = (5, -6)
the coordinate of F'' (3+3, 5-5) = (6, 0)
The diagram below shows the transformation of triangle DEF
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Let the total number of cars = 100
Total of sedan, van and sports cars = 39+33+7 = 79
Number of other cars = 100 - 79 = 21.
Let A be the event of owning a sedan,
B be the event of owning a van and
C be the event of owning a sports car.
D be the event of owning other cars.
Then,
and
Now,
p(non selection of van) = p(A ∪ C ∪ D)
= p(A) + p(C) + p(D)
= 0.67
The probability of none of the three selections would be a van is:
0.67 × 0.67 × 0.67
= 0.300763
=0.301
Hence, the correct option is (D).