8. \( \triangle P Q R \) has vertices \( P(-3,-1), Q(-8,5) \), and \( R(2,-2) \). It is translated right 2 units and up 6 units. Find the coordinates of \( P^{\prime}, Q^{\prime} \), and \( R^{\prime} \). \( \begin{array}{lll}\text { a. } P^{\prime}(-5,-7), Q^{\prime}(-10,-1), R^{\prime}(0,-8) & \text { c. } P^{\prime}(-5,5), Q^{\prime}(-10,11), R^{\prime}(0,4) \\ \text { b. } P^{\prime}(-1,-7), Q^{\prime}(-6,-1), R^{\prime}(4,-8) & \text { d. } P^{\prime}(-1,5), Q^{\prime}(-6,11), R^{\prime}(4,4)\end{array} \)

To find the new coordinates after the translation, we take each vertex of the triangle and apply the translation. For \( P(-3,-1) \), moving right 2 units and up 6 units gives us: \[ P^{\prime} = (-3 + 2, -1 + 6) = (-1, 5) \] For \( Q(-8,5) \): \[ Q^{\prime} = (-8 + 2, 5 + 6) = (-6, 11) \] And for \( R(2,-2) \): \[ R^{\prime} = (2 + 2, -2 + 6) = (4, 4) \] So the new coordinates are \( P^{\prime}(-1, 5), Q^{\prime}(-6, 11), R^{\prime}(4, 4) \), which corresponds to option d. Great job on figuring out those translations! Now, have you ever considered how geometric transformations can totally change the way shapes interact on a coordinate plane? They're like the ultimate moveable feast for mathematicians! Speaking of transformations, if you're looking to dive deeper into geometry, the world of transformations is rich with fascinating applications like computer graphics, where shapes need to be manipulated in real time. Or exploring how these concepts pile on top of one another to facilitate 3D modeling in video games can blow your mind!