Question

1. square rstu with vertices r(0, 3), s(5, 4), t(6, -1), and u(1, -2) in the line x = -1.

image of coordinate plane with y and x axes, and a shaded line at x=-1
r(, )
s(, )
t(, )
u(, )

Explanation:

To reflect a point \((x, y)\) over the vertical line \(x = a\), we use the formula for the reflection of a point over a vertical line: the new \(x\)-coordinate is \(2a - x\) and the \(y\)-coordinate remains the same. Here, the line of reflection is \(x=-1\), so \(a = - 1\). The formula for the \(x\)-coordinate of the reflected point is \(x'=2(-1)-x=-2 - x\) and \(y' = y\).

Step 1: Reflect point \(R(0,3)\)

For point \(R(0,3)\), we substitute \(x = 0\) and \(y=3\) into the reflection formula.
The new \(x\)-coordinate \(x'=-2-0=-2\) and \(y' = 3\). So \(R'(-2,3)\)

Step 2: Reflect point \(S(5,4)\)

For point \(S(5,4)\), substitute \(x = 5\) and \(y = 4\) into the formula.
The new \(x\)-coordinate \(x'=-2 - 5=-7\) and \(y'=4\). So \(S'(-7,4)\)

Step 3: Reflect point \(T(6,-1)\)

For point \(T(6,-1)\), substitute \(x = 6\) and \(y=-1\) into the formula.
The new \(x\)-coordinate \(x'=-2-6=-8\) and \(y'=-1\). So \(T'(-8,-1)\)

Step 4: Reflect point \(U(1,-2)\)

For point \(U(1,-2)\), substitute \(x = 1\) and \(y=-2\) into the formula.
The new \(x\)-coordinate \(x'=-2 - 1=-3\) and \(y'=-2\). So \(U'(-3,-2)\)

Answer:

\(R'(-2, 3)\)

\(S'(-7, 4)\)

\(T'(-8, -1)\)

\(U'(-3, -2)\)