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 D 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 = [tex]\sqrt{(-3 - (-2))^2 + (-4 - (-1))^2} = \sqrt{10}[/tex]
Therefore, length of MD' = 3·√10
Slope of MD, is given as follows;
- [tex]Slope, \ m = \dfrac{-1 - (-4)}{-2 - (-3)} = \dfrac{3}{1} = 3[/tex]
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 x, and y, are calculated as distance from the central point, M, 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:
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