The dot plots show rainfall totals for several spring
2 answers:
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The dilation of the rectangle stretches it with regards to the distances from the central point
The option that gives the coordinates of the point <em>D</em> is the option;
D (0, 5)
Reason:
The known parameter;
Coordinates of the center of dilation is M(-3, -4)
Scale factor of dilation = 3
The coordinates of the vertex of the rectangle ABCD are;
A(-2, 2), B(3, 2), C(3, -1), and D(-2, -1)
Length MD =
Therefore, length of MD' = 3·√10
Slope of MD, is given as follows;
Therefore, y = 3·x
x² + y² = (3·√10)²
x² + (3·x)² = (3·√10)²
10·x² = 90
x = 3
y = 9
We note that the value of <em>x</em>, and <em>y</em>, are calculated as distance from the central point, <em>M</em>, therefore;
The coordinates of the point D' is (-3 + x, -4 + y)
∴ Coordinates of D' = (-3 + 3, -4 + 9) = (0, 5)
- Coordinates of D' = (0, 5)
Learn more about dilation of a figure from a point here:
Answer:
Wire used for square is 7.55 m.
Step-by-step explanation:
Let the length of wire cut for square be 'x'.
Given:
Total length of the wire = 25 m
Length of wire for square = 'x'
Length of wire for equilateral triangle =
Now, area of square (a) =
Area of equilateral triangle (e) is given as:
Now, total area (A) is given as:
Now, in order to maximize 'A', the derivative of area with respect to 'x' must be 0.
∴
Therefore, the length of the wire that is cut for square should be 7.55 m for maximum area.