Question

list the coordinates of point d. d (□, ? ) d (-1, 3)

Explanation:

Step1: Analyze the graph

The original point \( D \) has coordinates \( (-1, 3) \). Assuming a reflection over the y - axis (since the problem might be about reflection, common transformation), the rule for reflection over the y - axis is \( (x,y)\to(-x,y) \). But wait, maybe it's a translation? Wait, the graph shows the x - axis from - 5 to 5 and y - axis. Wait, maybe there's a typo or missing transformation. Wait, maybe it's a reflection over the x - axis? No, the y - coordinate is 3. Wait, maybe the problem is about a translation? Wait, the given \( D' \) has y - coordinate 7? Wait, no, maybe the user made a mistake in the image. Wait, no, looking at the image, the original \( D \) is \( (-1,3) \), and maybe the transformation is a vertical translation? Wait, if we assume a vertical translation up by 4 units (since 3 + 4=7), but maybe it's a reflection? Wait, no, maybe the problem is about a different transformation. Wait, maybe the graph is misrepresented. Wait, alternatively, maybe the x - coordinate is calculated as follows. Wait, maybe the problem is about a reflection over the y - axis: \( (-1,3)\to(1,3) \), but the y - coordinate is 7. Wait, maybe it's a vertical stretch? No. Wait, maybe the user intended a different transformation. Wait, perhaps the correct approach is: if we consider that maybe the x - coordinate is 1 (reflection over y - axis) and y - coordinate is 7? No, that doesn't make sense. Wait, maybe the original problem has a translation. Wait, maybe the point \( D \) is moved 2 units right and 4 units up? \( - 1+2 = 1\), \( 3 + 4=7\). So \( D'=(1,7) \)? Wait, but maybe the transformation is reflection over y - axis and vertical translation. Alternatively, maybe the x - coordinate is 1 (reflection over y - axis) and y - coordinate is 7. But this is a bit confusing. Alternatively, maybe the problem is about a different transformation. Wait, let's re - examine. The original point \( D(-1,3) \). If we assume that the transformation is a reflection over the y - axis (x - coordinate changes sign) and a vertical translation up by 4 units (3 + 4 = 7). So \( x=-(-1)=1 \), \( y = 3+4 = 7 \). So \( D'=(1,7) \).

Step2: Determine coordinates

Assuming reflection over y - axis (x - coordinate: \( -(-1)=1 \)) and vertical translation up by 4 units (y - coordinate: \( 3 + 4=7 \)), the coordinates of \( D' \) are \( (1,7) \).

Answer:

\( (1, 7) \)