ΔABC has coordinates of A (–5, –7), B (6, –3), and C (2, 7). Find the coordinates of its image after a dilation centered at the origin with a scale factor of 2.

Question

A (–10, –14), B (12, –6), C (4, 14)

A (–5, –7), B (6, –3), C (2, 7)

A (–2.5, –3.5), B (3, –1.5), C (1, 3.5)

A (–10, –7), B (12, –3), C (4, 7)

Answer 1

To find the coordinates of the image of ΔABC after a dilation centered at the origin with a scale factor of 2, we multiply the coordinates of each vertex by the scale factor.

The vertices of the triangle are:

• A (–5, –7)
• B (6, –3)
• C (2, 7)

Now, applying the scale factor of 2:

1. For point A (–5, –7): \[ A' = (–5 \times 2, –7 \times 2) = (–10, –14) \]

2. For point B (6, –3): \[ B' = (6 \times 2, –3 \times 2) = (12, –6) \]

3. For point C (2, 7): \[ C' = (2 \times 2, 7 \times 2) = (4, 14) \]

Thus, the coordinates after the dilation are:

• A' (–10, –14)
• B' (12, –6)
• C' (4, 14)

The final result for the image after dilation is: A (–10, –14), B (12, –6), C (4, 14)

So the correct answer is: A (–10, –14), B (12, –6), C (4, 14).