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Coordinate Geometry — Maths STD 10 — Question

CBSE BoardEnglish MediumSTD 10MathsCoordinate Geometry1 Mark
MCQ
The line segment joining points $(-3, -4)$ and $(1, -2)$ is divided by $y-$axis in the ratio :
  • A
    $1 : 3$
  • B
    $2 : 3$
  • ✓
    $3 : 1$
  • D
    $2 : 3$
✓

Answer

Correct option: C.
$3 : 1$
The point lies on $y-$axis.
Its abscissa will be zero.
Let the point divides the line segment joining the points $(-3, -4)$ and $(1, -2)$ in the ratio $m : n$
$\therefore\ 0=\frac{\text{mx}_2+\text{nx}_1}{\text{m}+\text{n}}$
$\Rightarrow\ 0=\frac{\text{m}\times1+\text{n}\times(-3)}{\text{m}+\text{n}}$
$\Rightarrow\ \frac{\text{m}-3\text{n}}{\text{m}+\text{n}}=0$
$\Rightarrow\ \text{m}-3\text{n}=0$
$\Rightarrow\ \text{m}=3\text{n}$
$\Rightarrow\ \frac{\text{m}}{\text{n}}=\frac{3}{1}$
$\therefore$ Ratio $= 3 : 1$

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