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Standard VII

Mathematics

Angle Sum Property

Let ABC be a ...

Question

Let ABC be a triangle. Let A be the point (1,2) , y = x be the perpendicular bisector AB and x - 2y +1 =0 be the angle bisector of $∠ C$ . If the equation of BC is given by ax + by -5 =0, then the value of a + b is

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Solution

The correct option is B 2
For triangle ABC : A(1,2) and B=(2,1) is the image in y = x.The image of A(1,2) in the ine x-2y+1 =0 is given by
$\frac{x - 1}{1} = \frac{y - 2}{- 2} = \frac{4}{5}$
Hence, coordinates of point are $(\frac{9}{5}, \frac{2}{5})$
Since, this point lie on BC, therefore the equation of BC is
3x - y -5 = 0
$\Rightarrow a + b = 2$

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Angle Sum Property

Standard VII Mathematics

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Let ABC be a triangle. Let A be the point (1,2) , y = x be the perpendicular bisector AB and x - 2y +1 =0 be the angle bisector of ∠C. If the equation of BC is given by ax + by -5 =0, then the value of a + b is

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Let ABC be a triangle. Let A be the point (1,2) , y = x be the perpendicular bisector AB and x - 2y +1 =0 be the angle bisector of $∠ C$ . If the equation of BC is given by ax + by -5 =0, then the value of a + b is