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1 answer:
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Given:
The scale factor is and the center of dilation is at the point (4,2).
Red is original figure and green is dilated figure.
To find:
The coordinates of point C' and point A.
Solution:
Rule of dilation: If a figure is dilated with a scale factor k and the center of dilation is at the point (a,b), then
According to the given information, the scale factor is and the center of dilation is at (4,2).
...(i)
Let us assume the vertices of red triangle are A(m,n), B(10,14) and C(-2,11).
Using (i), we get
Therefore, the coordinates of Point C' are C'(2,5).
We assumed that point A is A(m,n).
Using (i), we get
From the given figure it is clear that the image of point A is (8,4).
On comparing both sides, we get
And,
Therefore, the coordinates of point A are (16,8).
Answer:
see the explanation
Step-by-step explanation:
we have
we know that
The radicand of the function cannot be a negative number
so
Solve for x
Multiply by -1 both sides
The domain of the function f(x) is the interval -----> (-∞, 0]
The domain is all real numbers less than or equal to zero
The range of the function f(x) is the interval ----> [0,∞)
The range is all real numbers greater than or equal to zero
<em>Example</em>
For x=144
----> is not true
This value of x not satisfy the domain
substitute
----> this value is undefined
For x=-144
----> is true
This value of x satisfy the domain
substitute
----> this value is defined
therefore
The function will be undefined for all those values of x that do not belong to the interval of the domain of the function