Triangle ABC

Question

has vertices point A (−2,4)
, point B (−6,8)
, and point C (−2,4)
. After dilation, triangle A′B′C′
has vertices point A′ (−1,2)
, point B′ (−3,4)
, and point C′ (−1,2)
. Determine the scale factor for the dilation of triangle ABC
with a center point of dilation at the origin (0,0)
. (1 point)
Responses

−12
negative Start Fraction 1 over 2 End Fraction

−2
negative 2

12
Start Fraction 1 over 2 End Fraction

2

Answer 1

To determine the scale factor for the dilation of triangle ABC to triangle A'B'C', we can use the formula:

\[ \text{Scale Factor} = \frac{\text{New Coordinate}}{\text{Old Coordinate}} \]

We can take any corresponding points from the two triangles.

Let's use points A and A':

• A: \((-2, 4)\)
• A': \((-1, 2)\)

Now let's calculate the scale factors for the x-coordinates and y-coordinates:

For the x-coordinate: \[ \text{Scale Factor (x)} = \frac{-1}{-2} = \frac{1}{2} \]

For the y-coordinate: \[ \text{Scale Factor (y)} = \frac{2}{4} = \frac{1}{2} \]

Both scale factors are equal, indicating consistent dilation. Therefore, the overall scale factor is \(\frac{1}{2}\).

Thus, the correct response is:

Start Fraction 1 over 2 End Fraction