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Straight Lines and Pair of Straight Lines question

2014 · Shift 0 · Q38

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Straight Lines and Pair of Straight Lines
2014 · Shift 0 · Q38

Straight Lines and Pair of Straight Lines question

2014 · Shift 0 · Q38

JEE MainMathematicsStraight Lines and Pair of Straight LinesMCQ+4 / −1

Let

PS

be the median of the triangle with vertices

P(2, 2)

,

Q(6, -1)

and

R(7, 3)

. The equation of the line passing through

(1, -1)

band parallel to PS is :

A
$4x + 7y + 3 = 0$
B
$2x - 9y - 11 = 0$
C
$4x - 7y - 11 = 0$
D
$2x + 9y + 7 = 0$

View written solutionFree

Correct answer: D

Find the midpoint $S$ of $QR$

Since $PS$ is a median, point $S$ is the midpoint of $Q(6,-1)$ and $R(7,3)$ .

S = \left(\frac{6+7}{2},\frac{-1+3}{2}\right)=\left(\frac{13}{2},1\right)

Find the slope of $PS$

Points on $PS$ are $P(2,2)$ and $S\left(\frac{13}{2},1\right)$ .

So the slope is

m = \frac{1-2}{\frac{13}{2}-2} = \frac{-1}{\frac{9}{2}} = -\frac{2}{9}

Equation of the line parallel to $PS$ and passing through $(1,-1)$

A line parallel to $PS$ has the same slope $-\frac{2}{9}$ .

Using point-slope form through $(1,-1)$ :

y-(-1)= -\frac{2}{9}(x-1)

y+1 = -\frac{2}{9}(x-1)

Multiply by $9$ :

9y+9 = -2x+2

2x+9y+7=0

Match with the options

The equation obtained is

2x+9y+7=0

This is Option D.

Comparison with stored correct answer

Stored correct answer: D

Our derived answer: D

So they agree.

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