Triangle RST has the coordinates shown below: \[ R(-2,1) \mathrm{S}(-8,2) \mathrm{T}(-4,5) \] 10) If triangle RST is translated 8 units right and 4 units down what are the coordinates of \( \mathrm{R}^{\prime} \) ? 11) If triangle RST is dilated by a scate factor of \( 1 / 2 \) what are the coordinates of T'? 12) If triangle RST if reflected across the \( y \)-axis what are the coordinates of \( S^{\prime} \) ?

To find the coordinates of \( R' \) after the translation, we take the original coordinates of \( R(-2,1) \) and apply the translation of 8 units to the right (add 8 to the x-coordinate) and 4 units down (subtract 4 from the y-coordinate). So, \[ R' = (-2+8, 1-4) = (6, -3). \] For point \( T \) after dilation by a scale factor of \( \frac{1}{2} \), we start from the original coordinates of \( T(-4, 5) \). The new coordinates are calculated by multiplying each coordinate by the scale factor: \[ T' = \left(-4 \times \frac{1}{2}, 5 \times \frac{1}{2}\right) = (-2, 2.5). \] Lastly, for point \( S \) after reflection across the \( y \)-axis, we will negate the x-coordinate of \( S(-8, 2) \): \[ S' = (8, 2). \] So the final answers are: 1. \( R' \): (6, -3) 2. \( T' \): (-2, 2.5) 3. \( S' \): (8, 2)