JAMB Mathematics 2023 Paper

Concept:Use the distance formula between two points and solve for the unknown coordinate.Explanation:Let $P(-3,-14) = (x_1, y_1)$ and $Q(t,-5) = (x_2, y_2)$.The distance $PQ$ is given as $9$ units.The distance formula is:$$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$Substitute the given coordinates into the formula:$$9 = \sqrt{(t - (-3))^2 + (-5 - (-14))^2}$$Simplify the expression inside the square root:$$9 = \sqrt{(t + 3)^2 + 9^2}$$$$9 = \sqrt{(t + 3)^2 + 81}$$Square both sides to remove the square root:$$81 = (t + 3)^2 + 81$$Subtract $81$ from both sides:$$(t + 3)^2 = 0$$Take the square root of both sides:$$t + 3 = 0$$Therefore:$$t = -3$$Answer:$t = -3$, which is option C.