Mathematics — Standard (041) — CBSE Class 10 board question

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)

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• 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.