Question

transformations test (topic 4) if the point ((x, y)) was translated 7 units to the left and 5 units down and then reflected across the x-axis, its new coordinates, in terms of (x) and (y) would be (\bigcirc (x - 7, -y + 5)) (\bigcirc (-x + 7, y + 5)) (\bigcirc (-x - 7, -y - 5)) (\bigcirc (x + 7, y + 5))

Explanation:

Step1: Translate 7 units left and 5 units down

To translate a point \((x, y)\) 7 units to the left, we subtract 7 from the \(x\)-coordinate. To translate it 5 units down, we subtract 5 from the \(y\)-coordinate. So after translation, the point becomes \((x - 7, y - 5)\).

Step2: Reflect across the x - axis

When we reflect a point \((a, b)\) across the \(x\)-axis, the \(x\)-coordinate remains the same and the \(y\)-coordinate changes its sign. So reflecting \((x - 7, y - 5)\) across the \(x\)-axis, we get \((x - 7, -(y - 5))\). Simplifying \(-(y - 5)\) gives \(-y + 5\). So the final coordinates are \((x - 7, -y + 5)\).

Answer:

\((x - 7, -y + 5)\) (the first option)