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Straight Lines — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsStraight Lines1 Mark
MCQ
Choose the correct answer.
If the line $\frac{\text{x}}{\text{a}} + \frac{\text{y}}{\text{b}} =1$ passes through the points $(2, -3)$ and $(4, -5),$ then $(a, b)$ is:
  • A
    $(1, 1)$
  • B
    $(-1, 1)$
  • C
    $(1, -1)$
  • ✓
    $(-1, -1)$
✓

Answer

Correct option: D.
$(-1, -1)$
Equation of line passing through the points $(2, -3)$ and $(4, -5)$ is
$\text{y}+3=\frac{-5+3}{4-2}(\text{x}-2)$
$\Rightarrow \text{y}+3=\frac{-2}{2}(\text{x}-2)$
$\Rightarrow \text{y}+3=-(\text{x}-2)$
$\Rightarrow \text{y}+3=-\text{x}+2$
$\Rightarrow \text{x}+\text{y}=-1$
$\Rightarrow \frac{\text{x}}{-1}+\frac{\text{y}}{-1}=1 ($intercept from$)$
$\therefore \text{a}=-1,\text{b}=-1$
Hence, the correct option is $(d).$

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