1. **State the problem:** We are given triangles \(\triangle LMN\) and \(\triangle PQR\) with coordinates: - \(L(1,2)\), \(M(3,2)\), \(N(3,5)\) - \(P(1,-5)\), \(Q(3,-5)\), \(R(3,-2)\) We need to: (i) Write down the coordinates of \(N\). (ii) Draw \(\triangle FGH\), the reflection of \(\triangle LMN\) in the y-axis. (iii) Describe the transformation mapping \(\triangle LMN\) onto \(\triangle PQR\) using vector notation. (iv) Complete the statement about the transformation mapping \(\triangle PQR\) onto \(\triangle FGH\). 2. **(i) Coordinates of \(N\):** From the problem, \(N = (3,5)\). 3. **(ii) Reflection of \(\triangle LMN\) in the y-axis:** Reflection in the y-axis changes \((x,y)\) to \((-x,y)\). So, \[ F = (-1,2),\quad G = (-3,2),\quad H = (-3,5) \] 4. **(iii) Transformation from \(\triangle LMN\) to \(\triangle PQR\):** Observe the coordinates: - \(L(1,2) \to P(1,-5)\) - \(M(3,2) \to Q(3,-5)\) - \(N(3,5) \to R(3,-2)\) The x-coordinates remain the same, y-coordinates change by subtracting 7: Vector notation for the transformation is a translation by vector \[ \vec{v} = \begin{pmatrix}0 \\ -7\end{pmatrix} \] So, \[ \triangle PQR = \triangle LMN + \vec{v} = \triangle LMN + \begin{pmatrix}0 \\ -7\end{pmatrix} \] 5. **(iv) Completing the statement:** "\(\triangle PQR\) is mapped onto \(\triangle FGH\) by a combination of two transformations. First, \(\triangle PQR\) is mapped onto \(\triangle LMN\) by a **translation**, parallel to the **y-axis**." **Final answers:** (i) \(N = (3,5)\) (ii) \(F(-1,2), G(-3,2), H(-3,5)\) (iii) Translation by vector \(\begin{pmatrix}0 \\ -7\end{pmatrix}\) (iv) Translation parallel to the y-axis