Question

42. Which matrix represents the image of the triangle with vertices at (-2,0), (1,5), and (4,-8) when dilated by a scale factor of 3?

Answer 1

The second matrix
`\left[\begin{array}{ccc}-6&3&12\\0&15&-24\end{array}\right]` represents the triangle dilated by a scale factor of 3.

Explanation:

Step 1:

To calculate the scale factor for any dilation, we divide the coordinates after dilation by the same coordinated before dilation.

The coordinates of a vertice are represented in the column of the matrix. Since there are three vertices, there are 2 rows with 3 columns. The order of the matrices is 2 × 3.

Step 2:

If we form a matrix with the vertices (-2,0), (1,5), and (4,-8), we get

`\left[\begin{array}{ccc}-2&1&4\\0&5&-8\end{array}\right]`

The scale factor is 3, so if we multiply the above matrix with 3 throughout, we will get the matrix that represents the vertices of the triangle after dilation.

Step 3:

The matrix that represents the triangle after dilation is given by

This is the second option.