If the distance between the points $(3, -5)$ and $(x, -5)$ is 15 units, then the values of $x$ are :

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Accepted Answer

## Model Answer Using the distance formula: $\sqrt{(x-3)^2 + (-5-(-5))^2} = 15$ $\Rightarrow |x - 3| = 15 \Rightarrow x - 3 = \pm 15 \Rightarrow x = 18$ or $x = -12$ The answer is **(b) $-12, 18$**. Source: Distance Formula, Chapter 7, Section 7.2 ## Explanation Since both points have the same y-coordinate (−5), the distance reduces to $|x - 3| = 15$. Solve both cases: $x - 3 = 15 \Rightarrow x = 18$ and $x - 3 = -15 \Rightarrow x = -12$. Watch the order in the options — the correct option lists $-12$ before $18$, which is option (b).

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