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: