Question

the given point is reflected across the line indicated. find the coordinates of the image. u across x = 1 if the given point u is reflected across the line x = 1, the image is (type an ordered pair.)

Explanation:

Step1: Find coordinates of U

From the graph, point U is at \((-3, -4)\) (assuming grid lines: x - coordinate is -3, y - coordinate is -4).

Step2: Use reflection formula over \(x = a\)

The formula for reflecting a point \((x,y)\) over the line \(x=a\) is \((2a - x,y)\). Here, \(a = 1\), \(x=-3\), \(y = - 4\).

Step3: Calculate the new x - coordinate

Substitute into the formula: \(2(1)-(-3)=2 + 3=5\). The y - coordinate remains the same, \(y=-4\).

Answer:

\((5, - 4)\)