1
MCQ (Single Correct Answer)

JEE Main 2019 (Online) 10th January Evening Slot

Two vertices of a triangle are (0, 2) and (4, 3). If its orthocenter is at the origin, then its third vertex lies in which quadrant
A
third
B
fourth
C
second
D
first

Explanation

mBD $$ \times $$ mAD = $$-$$ 1

$$ \Rightarrow $$  $$\left( {{{3 - 2} \over {4 - 0}}} \right) \times \left( {{{b - 0} \over {a - 0}}} \right) = - 1$$

$$ \Rightarrow $$  b + 4a = 0      . . . . (i)


mAB $$ \times $$ mCF = $$-$$ 1

$$ \Rightarrow $$  $$\left( {{{\left( {b - 2} \right)} \over {a - 0}}} \right) \times \left( {{3 \over 4}} \right) = - 1$$

$$ \Rightarrow $$  3b $$-$$ 6 = $$-$$ 4a

$$ \Rightarrow $$  4a + 3b = 6      . . . . .(ii)

From (i) and (ii)

a = $${{ - 3} \over 4}$$, b = 3

$$ \therefore $$  IInd quadrant.
2
MCQ (Single Correct Answer)

JEE Main 2019 (Online) 11th January Evening Slot

If in a parallelogram ABDC, the coordinates of A, B and C are respectively (1, 2), (3, 4) and (2, 5), then the equation of the diagonal AD is :
A
5x + 3y – 11 = 0
B
5x – 3y + 1 = 0
C
3x – 5y + 7 = 0
D
3x + 5y – 13 = 0

Explanation

co-ordinates of point D are (4, 7)

$$ \Rightarrow $$  line AD is 5x $$-$$ 3y + 1 = 0
3
MCQ (Single Correct Answer)

JEE Main 2019 (Online) 12th January Morning Slot

If the straight line, 2x – 3y + 17 = 0 is perpendicular to the line passing through the points (7, 17) and (15, $$\beta $$), then $$\beta $$ equals :
A
$${{35} \over 3}$$
B
$$-$$ 5
C
$$-$$ $${{35} \over 3}$$
D
5

Explanation

$${{17 - \beta } \over { - 8}} \times {2 \over 3} = - 1$$

$$\beta $$ = 5
4
MCQ (Single Correct Answer)

JEE Main 2019 (Online) 12th January Evening Slot

If a straight line passing through the point P(–3, 4) is such that its intercepted portion between the coordinate axes is bisected at P, then its equation is :
A
x – y + 7 = 0
B
4x – 3y + 24 = 0
C
4x + 3y = 0
D
3x – 4y + 25 = 0

Explanation


Let the line be $${x \over a} + {y \over b} = 1$$

($$-$$ 3, 4) = $$\left( {{a \over 2},{b \over 2}} \right)$$

a = $$-$$6, b = 8

equation of line is 4x $$-$$ 3y + 24 = 0

Questions Asked from Straight Lines and Pair of Straight Lines

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