Question

reflect the given triangle over the line y = -x.
\\( \

$$\begin{bmatrix} 0 & 7 & -1 \\\\ 0 & -3 & -4 \\end{bmatrix}$$

\\)
\\( \

$$\begin{bmatrix} 0 & 3 & 4 \\\\ 0 & -7 & \\text{?} \\end{bmatrix}$$

\\)

Explanation:

Step1: Recall the reflection formula over \(y = -x\)

When reflecting a point \((x,y)\) over the line \(y=-x\), the transformation rule is \((x,y)\to(-y, -x)\).

Step2: Apply the formula to the point \((-1,-4)\)

For the point with \(x=-1\) and \(y = -4\), using the rule \((x,y)\to(-y,-x)\):
Substitute \(x=-1\) and \(y=-4\) into \(-y\) and \(-x\).
We get \(-y=-(-4) = 4\) and \(-x=-(-1)=1\)

Answer:

\(1\)