Question

write the coordinates of the vertices after a dilation with a scale factor of $\frac{1}{2}$, centered at the origin.

Explanation:

Step1: Identify original coordinates

The original coordinates of point L are (4, 4) and of point M are (8, 4).

Step2: Apply dilation formula

For a dilation centered at the origin with scale - factor \(k=\frac{1}{2}\), the new coordinates \((x',y')\) of a point \((x,y)\) are given by \(x' = kx\) and \(y'=ky\).
For point L:
\(x_L'=\frac{1}{2}\times4 = 2\)
\(y_L'=\frac{1}{2}\times4 = 2\)
For point M:
\(x_M'=\frac{1}{2}\times8 = 4\)
\(y_M'=\frac{1}{2}\times4 = 2\)

Answer:

The new coordinates of L are (2, 2) and of M are (4, 2)