Question

the dashed figure is the image of the solid figure. what is the algebraic notation for the translation? (x, y) --> (x - 7, y + 4) (x, y) --> (4x, 7y) (x, y) --> (x + 7, y - 4) (x, y) --> (x + 4, y + 7)

Explanation:

Step1: Analyze translation concept

Translation in coordinate - plane moves a figure horizontally and vertically. The algebraic notation for a translation is \((x,y)\to(x + a,y + b)\), where \(a\) is the horizontal displacement and \(b\) is the vertical displacement.

Step2: Determine horizontal displacement

To find the horizontal displacement, we look at how the \(x\) - coordinate changes. If the figure moves to the right, \(a>0\), and if it moves to the left, \(a < 0\).

Step3: Determine vertical displacement

To find the vertical displacement, we look at how the \(y\) - coordinate changes. If the figure moves up, \(b>0\), and if it moves down, \(b < 0\).

Step4: Check each option

• For \((x,y)\to(x - 7,y + 4)\): It means moving 7 units to the left (\(x\) - coordinate decreases by 7) and 4 units up (\(y\) - coordinate increases by 4).
• For \((x,y)\to(4x,7y)\): This is a dilation, not a translation.
• For \((x,y)\to(x + 7,y - 4)\): It means moving 7 units to the right (\(x\) - coordinate increases by 7) and 4 units down (\(y\) - coordinate decreases by 4).
• For \((x,y)\to(x + 4,y + 7)\): It means moving 4 units to the right (\(x\) - coordinate increases by 4) and 7 units up (\(y\) - coordinate increases by 7).

Answer:

Without seeing the actual graph to determine the direction and magnitude of the translation, we can't be sure. But if we assume the solid - to - dashed figure moves 7 units to the left and 4 units up, the answer is \((x,y)\to(x - 7,y + 4)\)