CBSE BoardEnglish MediumSTD 10MathsCoordinate Geometry1 Mark
MCQ
If the points $A (1,2), O (0,0)$ and $C ( a , b )$ are collinear then
A
$a = b$
B
$a =2 b$
✓
$2 a = b$
D
$a + b =0$
✓
Answer
Correct option: C.
$2 a = b$
Here, $\left( x _1=1, y _2=2\right),\left( x ^2=0, y ^2=0\right)$ and ( $x _3= a , y _3= b$ ).
Since the given points are collinear, we have
$x_1\left(y_2-y_3\right)+x_2\left(y_3-y_1\right)+x_3\left(y_1-y_2\right)=0$
$\Rightarrow 1 \cdot(0-b)+0 \cdot(b-2)+a(2-0)=0$
$\Rightarrow-b+0+2 a=0$
$\Rightarrow 2 a=b$
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