Question

A

Answer 1

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 = $\sqrt{(-3 - (-2))^2 + (-4 - (-1))^2} = \sqrt{10}$

Therefore, length of MD' = 3·√10

Slope of MD, is given as follows;

• $Slope, \ m = \dfrac{-1 - (-4)}{-2 - (-3)} = \dfrac{3}{1} = 3$

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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