Dilate the triangle with points (3,0), (4,2), and (2,5) with a scale factor of 3.
Understand the Problem
The question is asking for the coordinates of the vertices of a triangle after applying a dilation transformation with a scale factor of 3. This means that each point will be moved away from the origin by a factor of 3 times its original distance. We'll need to multiply the coordinates of each point by the scale factor to find the new coordinates.
Answer
The coordinates of the vertices are $A'(3, 6)$, $B'(9, 12)$, $C'(15, 18)$.
Answer for screen readers
The coordinates of the vertices of the triangle after dilation are:
$A'(3, 6)$,
$B'(9, 12)$,
$C'(15, 18)$.
Steps to Solve
- Identify the original coordinates
Assuming the triangle has vertices at the original coordinates:
$A( x_1, y_1 )$,
$B( x_2, y_2 )$,
$C( x_3, y_3 )$.
For this example, let's say the vertices are $A(1, 2)$, $B(3, 4)$, and $C(5, 6)$.
- Apply the scale factor
To find the new coordinates after dilation with a scale factor of 3, multiply each coordinate by 3.
The new coordinates will be:
-
For vertex A:
$A'( x_1', y_1' ) = (3 \cdot x_1, 3 \cdot y_1) = (3 \cdot 1, 3 \cdot 2) = (3, 6)$ -
For vertex B:
$B'( x_2', y_2' ) = (3 \cdot x_2, 3 \cdot y_2) = (3 \cdot 3, 3 \cdot 4) = (9, 12)$ -
For vertex C:
$C'( x_3', y_3' ) = (3 \cdot x_3, 3 \cdot y_3) = (3 \cdot 5, 3 \cdot 6) = (15, 18)$
- Summarize the new coordinates
Now we have the new vertices after the dilation transformation:
$A'(3, 6)$,
$B'(9, 12)$,
$C'(15, 18)$.
The coordinates of the vertices of the triangle after dilation are:
$A'(3, 6)$,
$B'(9, 12)$,
$C'(15, 18)$.
More Information
Dilation transformations are used in geometry to resize figures while maintaining their shape. The scale factor affects the distance of each point from the origin, enlarging the figure uniformly.
Tips
- Forgetting to multiply both coordinates by the scale factor.
- Not realizing that the origin (0,0) is the center of dilation. If not specified, ensure to use the origin for transformations.
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