1. **Reflect the polygon against the x-axis** with points (4,6), (8,16), (4,10), (8,20). Reflection about the x-axis changes a point $(x,y)$ to $(x,-y)$. - For $(4,6)$, reflection is $(4,-6)$. - For $(8,16)$, reflection is $(8,-16)$. - For $(4,10)$, reflection is $(4,-10)$. - For $(8,20)$, reflection is $(8,-20)$. 2. **Rotate triangle A(2,2), B(8,2), C(5,5) by 90° anti-clockwise**. Rotation formula for 90° anti-clockwise: $(x,y) \to (-y,x)$. - $A(2,2) \to (-2,2)$ - $B(8,2) \to (-2,8)$ - $C(5,5) \to (-5,5)$ 3. **Rotate point $P=(5,1)$ about origin by 90°**. Using the same rotation formula: $(5,1) \to (-1,5)$. 4. **Basic design of magnetic deflection CRT** (conceptual explanation): - Electron beam is emitted from the electron gun. - Magnetic coils create magnetic fields perpendicular to the beam. - These fields deflect the beam horizontally and vertically. - The deflected beam hits the phosphor screen to create images. 5. **DDA line drawing algorithm procedure:** - Calculate differences: $dx = x_1 - x_0$, $dy = y_1 - y_0$. - Determine steps = max$(|dx|, |dy|)$. - Calculate increments: $x_{inc} = \frac{dx}{steps}$, $y_{inc} = \frac{dy}{steps}$. - Initialize $x = x_0$, $y = y_0$. - For each step, plot $(round(x), round(y))$, then update $x = x + x_{inc}$, $y = y + y_{inc}$. **Example DDA program in Python:** ```python def dda(x0, y0, x1, y1): dx = x1 - x0 dy = y1 - y0 steps = max(abs(dx), abs(dy)) x_inc = dx / steps y_inc = dy / steps x, y = x0, y0 points = [] for _ in range(int(steps) + 1): points.append((round(x), round(y))) x += x_inc y += y_inc return points ``` **Final answers:** - Reflected polygon points: $(4,-6), (8,-16), (4,-10), (8,-20)$. - Rotated triangle points: $A'(-2,2), B'(-2,8), C'(-5,5)$. - Rotated point $P'$: $(-1,5)$.