First slide

Equation of line in Straight lines

Question

The equation of an altitude of an equilateral triangle is $\sqrt{3} x + y = 2 \sqrt{3}$ and one of its vertices is $(3, \sqrt{3})$ then

Moderate

Question

The possible number of triangle(s) is

Solution

C is image of B w.r.t. $\sqrt{3} x + y - 2 \sqrt{3} = 0$
$A = (0, 2 \sqrt{3}), A^{'}$ $B C$ is image of A w.r.t. .
Equation of allitude AD is $\sqrt{3} x + y - 2 \sqrt{3} = 0$
The image of point B about the line AD is (0, 0)
$∴ B C = 2 \sqrt{3}$ Clearly $(2 \sqrt{3}, 0)$ is not a vertex of triangle

Question

Which of the following can not be the vertex of the triangle

A

(0,0)
B

$(0, 2 \sqrt{3})$
C

$(3, - \sqrt{3})$
D

$(2 \sqrt{3}, 0)$

Solution

C is image of B w.r.t. $\sqrt{3} x + y - 2 \sqrt{3} = 0$
$A = (0, 2 \sqrt{3}), A^{'}$ $B C$ is image of A w.r.t. .
Equation of allitude AD is $\sqrt{3} x + y - 2 \sqrt{3} = 0$
The image of point B about the line AD is (0, 0)
$∴ B C = 2 \sqrt{3}$ Clearly $(2 \sqrt{3}, 0)$ is not a vertex of triangle

Question

Which of the following can be the possible orthocentre of the triangle

A

$(1, \sqrt{3})$
B

$(0, \sqrt{3})$
C

$(0, 2)$
D

$(0, 3)$

Solution

C is image of B w.r.t. $\sqrt{3} x + y - 2 \sqrt{3} = 0$
$A = (0, 2 \sqrt{3}), A^{'}$ $B C$ is image of A w.r.t. .
Equation of allitude AD is $\sqrt{3} x + y - 2 \sqrt{3} = 0$
The image of point B about the line AD is (0, 0)
$∴ B C = 2 \sqrt{3}$ Clearly $(2 \sqrt{3}, 0)$ is not a vertex of triangle

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