JAMB Mathematics 2014 Paper

Concept:The midpoint of a line segment between the two axes is found by locating the intercepts of the line on the x-axis and y-axis, then applying the midpoint formula.Explanation:On the x-axis, $y = 0$.Substitute into $y - 4x + 3 = 0$:$0 - 4x + 3 = 0$$-4x = -3$$x = \frac{3}{4}$So the line cuts the x-axis at $\left(\frac{3}{4}, 0\right)$.On the y-axis, $x = 0$.Substitute into the equation:$y - 4(0) + 3 = 0$$y + 3 = 0$$y = -3$So the line cuts the y-axis at $(0, -3)$.The midpoint $M$ is calculated as:$M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$$M = \left(\frac{\frac{3}{4} + 0}{2}, \frac{0 + (-3)}{2}\right)$$M = \left(\frac{\frac{3}{4}}{2}, \frac{-3}{2}\right)$$M = \left(\frac{3}{8}, \frac{-3}{2}\right)$Answer:Option A: $\left(\frac{3}{8}, \frac{-3}{2}\right)$.