1. **State the problem:** We are given two lines, l and k, and need to draw them on a coordinate diagram, find their intersection point R, and then find the area of triangle RST formed by points R and the x-intercepts S and T of lines l and k. 2. **Find the equations of lines l and k:** (Since the user did not provide explicit equations, we assume they are given or need to be found from context. For demonstration, let's assume line l: $y = m_1x + c_1$ and line k: $y = m_2x + c_2$.) 3. **Find the point of intersection R:** Set the two line equations equal to find $x$: $$m_1x + c_1 = m_2x + c_2$$ Rearranged: $$m_1x - m_2x = c_2 - c_1$$ $$x(m_1 - m_2) = c_2 - c_1$$ Divide both sides by $m_1 - m_2$ (assuming $m_1 \neq m_2$): $$x = \frac{c_2 - c_1}{m_1 - m_2}$$ Substitute $x$ back into either line equation to find $y$: $$y = m_1 \times x + c_1$$ 4. **Find x-intercepts S and T:** Set $y=0$ in each line equation: For line l: $$0 = m_1x + c_1 \Rightarrow x = -\frac{c_1}{m_1}$$ For line k: $$0 = m_2x + c_2 \Rightarrow x = -\frac{c_2}{m_2}$$ Points: $$S = \left(-\frac{c_1}{m_1}, 0\right), \quad T = \left(-\frac{c_2}{m_2}, 0\right)$$ 5. **Calculate area of triangle RST:** Using the formula for area of triangle with vertices $(x_1,y_1)$, $(x_2,y_2)$, $(x_3,y_3)$: $$\text{Area} = \frac{1}{2} \left| x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) \right|$$ Substitute: $$R = (x_R, y_R), S = \left(-\frac{c_1}{m_1}, 0\right), T = \left(-\frac{c_2}{m_2}, 0\right)$$ Area: $$= \frac{1}{2} \left| x_R(0 - 0) + \left(-\frac{c_1}{m_1}\right)(0 - y_R) + \left(-\frac{c_2}{m_2}\right)(y_R - 0) \right|$$ $$= \frac{1}{2} \left| \frac{c_1}{m_1} y_R - \frac{c_2}{m_2} y_R \right| = \frac{1}{2} |y_R| \left| \frac{c_1}{m_1} - \frac{c_2}{m_2} \right|$$ **Summary:** - Find intersection $R$ by solving line equations. - Find x-intercepts $S$ and $T$ by setting $y=0$. - Calculate area of triangle $RST$ using the formula above. Since no explicit line equations were provided, this is the general method to solve the problem. --- **Question 2(a):** Given circle equation: $$ (x - 4)^2 + (y + 3)^2 = 25 $$ - Centre is at $(4, -3)$. - Radius is $\sqrt{25} = 5$. **Question 2(b):** Check if point $P(7, -7)$ lies on the circle: Substitute into circle equation: $$ (7 - 4)^2 + (-7 + 3)^2 = 3^2 + (-4)^2 = 9 + 16 = 25 $$ Since left side equals right side, point $P$ lies on the circle.