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JEE MATHEMATICS MCQ: STRAIGHT LINES

1 Easy

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Application +4 | -1

The vertices of a family of triangles have integer coordinates. If two of the vertices of all the triangles are (0, 0) and (6, 8), then the least value of areas of the triangles is

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Correct option: A

1

Option A (1) is correct because the minimum area of the triangle with integer coordinates is obtained when the third vertex is (1,1), resulting in an area of 1.

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If the three lines

x-3 y=p, a x+2 y=q

a x+y=r

form a right-angled triangle then :
The orthocentre of the triangle whose vertices are

\left\{ {a{t_1}{t_2},\;a\left( {{t_1} + {t_2})\} ,\{ a{t_2}{t_3},a({t_2} + {t_3}} \right)} \right\},\;\left\{ {a{t_3}{t_1},\;a\left( {{t_3} + {t_1}} \right)} \right\}

is
The distance between the parallel lines

y = 2\;x + 4

6x = 3y + 5

is The distance between the pair of lines given by

{x^2} + {y^2} + 2xy - 8ax - 8ay - 9{a^2} = 0

is Find the image of the point

(3,8)

with respect of the line

x+3 y=7

assuming the line to be plane mirror: The centroid of the triangle whose three sides are given by the combined equation

\left( {{x^2} + 7xy + 2{y^2}} \right)\left( {y - 1} \right) = 0