Triangle ABC has vertices A(2, 1) , B(3, 0) , and C(1, −2) . Graph the triangle and its image after a dilation with a scale factor of 3.
To graph the triangle ABC and its image after a dilation with a scale factor of 3, follow these steps:
1. Plot the original triangle ABC:
- Point A(2, 1): Start at the origin on your graph paper and move 2 units to the right (x-axis) and 1 unit upwards (y-axis). Mark this point as A(2, 1).
- Point B(3, 0): Start from A and move 1 unit to the right and 0 units upwards. Mark this point as B(3, 0).
- Point C(1, -2): Start from B and move 2 units downwards. Mark this point as C(1, -2).
Connect the three points A, B, and C to form the triangle ABC.
2. To create the image of the triangle after a dilation with a scale factor of 3, multiply the coordinates of each point (A, B, and C) by the scale factor:
- Point A(2, 1) --> Image A'(6, 3) [Scale each coordinate by 3]
- Point B(3, 0) --> Image B'(9, 0) [Scale each coordinate by 3]
- Point C(1, -2) --> Image C'(3, -6) [Scale each coordinate by 3]
3. Plot the image triangle A'B'C':
- Point A' (6, 3): Start at the origin and move 6 units to the right (x-axis) and 3 units upwards (y-axis). Mark this point as A'.
- Point B' (9, 0): Start from A' and move 3 units to the right and 0 units upwards. Mark this point as B'.
- Point C' (3, -6): Start from B' and move 6 units downwards. Mark this point as C'.
Connect the three points A', B', and C' to form the image triangle A'B'C'.
4. Label the original triangle ABC and its image A'B'C' on the graph paper to complete the graph