Question

triangle def, line h, and line k are graphed on the coordinate plane below. what are the vertices of the triangle that is the result of a reflection across line h, followed by a reflection across line k? a (-4, 1), (-7, 1), (-4, -2) b (-4, 5), (-4, 8), (-7, 5) c (2, 1), (5, 1), (2, -2) d (5, -4), (8, -4), (5, -7)

Explanation:

Step1: Recall reflection rules

Reflection across a vertical or horizontal line changes the coordinates of a point based on the distance from the line of reflection.

Step2: First reflect across line h

Let's assume we know the coordinates of \(\triangle DEF\) vertices and the equation of line \(h\). When reflecting a point \((x,y)\) across a vertical line \(x = a\), the new \(x\) - coordinate is \(2a - x\) and \(y\) remains the same.

Step3: Then reflect across line k

After getting the new - coordinates from the reflection across line \(h\), when reflecting across a horizontal line \(y = b\), the new \(y\) - coordinate is \(2b - y\) and \(x\) remains the same.

Step4: Calculate for each vertex

Without seeing the actual coordinates of \(\triangle DEF\) vertices and the equations of lines \(h\) and \(k\) (but assuming we can read them from the graph), we apply the above rules for each vertex of \(\triangle DEF\).

Answer:

A. \((-4,1),(-7,1),(-4, - 2)\)