A line intersects y-axis and x-axis at point P and Q, respectively. If R(2, 5) is the mid-point of line segment PQ, then find the coordinates of P and Q.
Generated by claude-sonnet-4-6 · 2026-06-15 10:31 · grounding rag
Model Answer
Let P lie on the y-axis ⇒ P = (0, y₁), and Q lie on the x-axis ⇒ Q = (x₂, 0).
R(2, 5) is the mid-point of PQ, so using the mid-point formula:
$$\frac{0 + x_2}{2} = 2 \Rightarrow x_2 = 4$$
$$\frac{y_1 + 0}{2} = 5 \Rightarrow y_1 = 10$$
Therefore, P = (0, 10) and Q = (4, 0).
Source: Chapter 7, Section 7.3 (Mid-point Formula)
---
Explanation
- A point on the y-axis has x-coordinate = 0; a point on the x-axis has y-coordinate = 0. This is stated in Section 7.1.
- Apply the mid-point formula: set each component equal to the given mid-point coordinates and solve — this is the key step examiners look for.
- Both coordinates of P and Q must be stated clearly for full marks.