Question

Given the coordinates of the triangle, determine the coordinates of its image after a dilation with the given scale factor centered at the origin. S 20. A(0, 3), B(6, 0), C(0, -3); scale factor: 1/3​

Answer 1

Answer: The image of the triangle after the dilation with a scale factor of 1/3 centered at the origin is A'(0, 1), B'(2, 0), and C'(0, -1).

Explanation:

To find the coordinates of the triangle's image after a dilation with a scale factor of 1/3 centered at the origin, you can multiply the x and y coordinates of each vertex by the scale factor.

Let's calculate the new coordinates for each vertex:

A(0, 3):

New x-coordinate: 0 * (1/3) = 0

New y-coordinate: 3 * (1/3) = 1

So, the new coordinates for A are (0, 1).

B(6, 0):

New x-coordinate: 6 * (1/3) = 2

New y-coordinate: 0 * (1/3) = 0

So, the new coordinates for B are (2, 0).

C(0, -3):

New x-coordinate: 0 * (1/3) = 0

New y-coordinate: -3 * (1/3) = -1

So, the new coordinates for C are (0, -1).

The image of the triangle after the dilation with a scale factor of 1/3 centered at the origin is A'(0, 1), B'(2, 0), and C'(0, -1).