Question

draw the reflection of the following triangle over the line m.

Explanation:

Step1: Find the distance of each vertex from line \(m\)

Let's assume the vertices of the triangle are \(A\), \(B\), \(C\). For a point \((x,y)\) and the line \(x = 0\) (assuming line \(m\) is the \(y -\)axis, since it's a vertical line through the origin in the given graph). The distance of a point \((x,y)\) from the line \(x = 0\) is \(|x|\).

Step2: Reflect each vertex across line \(m\)

If a point has coordinates \((x,y)\) and we reflect it over the line \(x = 0\) (line \(m\)), the rule for reflection is \((x,y)\to(-x,y)\). For example, if a vertex is at \((- 3,-5)\), its reflection is \((3,-5)\); if a vertex is at \((-1,0)\), its reflection is \((1,0)\); if a vertex is at \((-4,-2)\), its reflection is \((4,-2)\)

Step3: Connect the reflected vertices

Use a straight - edge to connect the reflected vertices to form the reflected triangle.

Answer:

Draw the triangle with vertices obtained by reflecting the original triangle's vertices across line \(m\) (using the rule \((x,y)\to(-x,y)\) if \(m\) is the \(y -\)axis) and connect them.