Question

determine the translation. use non - negative numbers. a translation by \boxed{} units to the \boxed{left} and \boxed{} units \boxed{down} 1/3 every point in a translated figure moves the same distance and direction. lets select a point to examine. 2/3 we see that point c moved 8 units to the left and 5 units up to form the image c.

Explanation:

Step1: Analyze horizontal translation

From the given information, point \( C \) moved 8 units to the left. So the horizontal translation (left/right) has a magnitude of 8 units (since we use non - negative numbers for the number of units, and the direction is left).

Step2: Analyze vertical translation

Wait, there is a mistake in the initial thought. Wait, the problem's dropdown for vertical is "down" but the hint says point \( C \) moved 5 units up. But maybe there is a mis - reading. Wait, no, let's re - check. Wait, the user's problem: the first box is for the number of units (horizontal), the second dropdown is left/right, the third box is for vertical units, and the fourth dropdown is up/down. But the hint says "We see that point \( C \) moved 8 units to the left and 5 units up to form the image \( C' \)". But the vertical dropdown in the problem is "down" which might be a typo, but according to the hint, for the horizontal (left) the number of units is 8, and for the vertical (if we follow the hint, but the dropdown is down, maybe it's a mistake, but according to the hint, the vertical movement is 5 units (but direction is up, but the dropdown is down, maybe the problem has a different point). Wait, no, the problem says "Use non - negative numbers" for the units. So for the horizontal translation (left), the number of units is 8, and for the vertical, if we take the hint, it's 5, but the dropdown is down. Maybe the problem's dropdown is incorrect, but according to the hint, the horizontal units (left) is 8, and vertical units (up) is 5, but the problem's vertical dropdown is "down" which is conflicting. But maybe it's a mistake in the problem, and we follow the hint. So the first box (horizontal units) is 8, the third box (vertical units) is 5. But let's check again. The problem statement: "A translation by [first box] units to the [left/right dropdown] and [third box] units [up/down dropdown]". The hint says point \( C \) moved 8 units left and 5 units up. So:

Step1: Horizontal translation units

The horizontal movement (left) has 8 units (non - negative), so the first box is 8.

Step2: Vertical translation units

The vertical movement (up) has 5 units (non - negative), so the third box is 5.

Answer:

First box: 8, Third box: 5