If the mid-point of the line segment joining the points $A(3, 4)$ and $B(k, 6)$ is $P(x, y)$ and $x + y - 10 = 0$, then find the value of $k$.
Generated by claude-sonnet-4-6 · 2026-06-15 10:28 · grounding rag
Model Answer
Mid-point of A(3, 4) and B(k, 6) is P(x, y).
Using the mid-point formula:
$$x = \frac{3 + k}{2}, \quad y = \frac{4 + 6}{2} = \frac{10}{2} = 5$$
Since $x + y - 10 = 0$:
$$x + 5 - 10 = 0 \implies x = 5$$
Now, $x = \dfrac{3 + k}{2}$:
$$5 = \frac{3 + k}{2} \implies 10 = 3 + k \implies k = 7$$
∴ The value of k = 7.
Source: Chapter 7 — Coordinate Geometry, Section 7.3 (Mid-point Formula)
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Explanation
- The mid-point formula gives coordinates $\left(\dfrac{x_1+x_2}{2},\ \dfrac{y_1+y_2}{2}\right)$.
- Find y first (it has no unknown), substitute into the given condition to get x, then use x to find k.
- Examiners award 1 mark for correct mid-point expressions, 1 mark for finding x and y, and 1 mark for the correct value of k. Show all steps clearly.