Question

3 fill in the blank. 8 points map the coordinates of the reflection of square u m n o with vertices u(-4, 6), m(-1, 8), n(1, 5), and o(-2, 3) in the line y + 2 grid image of square and horizontal line included

Explanation:

To reflect a point \((x, y)\) over the line \(y = k\), the formula for the reflected point \((x', y')\) is \(x'=x\) and \(y' = 2k - y\). Here, \(k = 2\), so the formula becomes \(y'=4 - y\) and \(x' = x\).

Step 1: Reflect point \(U(-4,6)\)

Using the formula \(x'=-4\), \(y' = 4 - 6=-2\). So the reflected point \(U'\) is \((-4,-2)\).

Step 2: Reflect point \(M(-1,8)\)

Using the formula \(x'=-1\), \(y' = 4 - 8=-4\). So the reflected point \(M'\) is \((-1,-4)\).

Step 3: Reflect point \(N(1,5)\)

Using the formula \(x' = 1\), \(y'=4 - 5=-1\). So the reflected point \(N'\) is \((1,-1)\).

Step 4: Reflect point \(O(-2,3)\)

Using the formula \(x'=-2\), \(y' = 4 - 3 = 1\). So the reflected point \(O'\) is \((-2,1)\).

Answer:

The reflected coordinates are \(U'(-4, -2)\), \(M'(-1, -4)\), \(N'(1, -1)\), \(O'(-2, 1)\)