Question

graph the image of p(4, 7) after a translation along < 1, -9 > and a reflection in x = 2. point clear undo

Explanation:

Step1: Perform the translation

To translate a point \((x, y)\) along the vector \(\langle a, b
angle\), we use the rule \((x + a, y + b)\). For point \(P(4, 7)\) and vector \(\langle 1, -9
angle\), we calculate the new coordinates:
\(x = 4 + 1 = 5\)
\(y = 7 + (-9) = -2\)
So after translation, the point is \((5, -2)\).

Step2: Perform the reflection over \(x = 2\)

The rule for reflecting a point \((x, y)\) over the vertical line \(x = h\) is \((2h - x, y)\). Here, \(h = 2\) and the point after translation is \((5, -2)\).
Calculate the new \(x\)-coordinate:
\(x' = 2(2) - 5 = 4 - 5 = -1\)
The \(y\)-coordinate remains the same: \(y' = -2\)

Answer:

The image of \(P(4, 7)\) after the given transformations is \((-1, -2)\)