SATHEE: Straight Line and Pair of Straight Lines 1 Question 58

Straight Line and Pair of Straight Lines 1 Question 58

58. Straight lines $3 x + 4 y = 5$ and $4 x - 3 y = 15$ intersect at the point $A$ . Points $B$ and $C$ are chosen on these two lines such that $A B = A C$ . Determine the possible equations of the line $B C$ passing through the point $(1, 2)$ .

$(1990, 4$ M)

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Solution:

Let $m_{1}$ and $m_{2}$ be the slopes of the lines $3 x + 4 y = 5$ and $4 x - 3 y = 15$ , respectively.

Then, $m_{1} = - \frac{3}{4}$ and $m_{2} = \frac{4}{3}$

Clearly, $m_{1} m_{2} = - 1$ . So, lines $A B$ and $A C$ are at right angle. Thus, the $△ A B C$ is a right angled isosceles triangle.

Hence, the line $B C$ through $(1, 2)$ will make an angle of $45^{\circ}$ with the given lines. So, the possible equations of $B C$ are

$(y - 2) = \frac{m \pm \tan 45^{\circ}}{1 \mp m \tan 45^{\circ}} (x - 1)$

where, $m =$ slope of $A B = - \frac{3}{4}$

$\begin{aligned} \Rightarrow (y - 2) = \frac{- \frac{3}{4} \pm 1}{1 \mp - \frac{3}{4}} (x - 1) \\ \Rightarrow (y - 2) = \frac{- 3 \pm 4}{4 \pm 3} (x - 1) \\ \Rightarrow (y - 2) = \frac{1}{7} (x - 1) \\ and (y - 2) = - 7 (x - 1) \\ \Rightarrow x - 7 y + 13 = 0 \\ and 7 x + y - 9 = 0 \end{aligned}$

Straight Line and Pair of Straight Lines 1 Question 58

58. Straight lines $3 x + 4 y = 5$ and $4 x - 3 y = 15$ intersect at the point $A$ . Points $B$ and $C$ are chosen on these two lines such that $A B = A C$ . Determine the possible equations of the line $B C$ passing through the point $(1, 2)$ .

Solution:

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Straight Line and Pair of Straight Lines 1 Question 58

58. Straight lines 3x+4y=5 and 4x−3y=15 intersect at the point A. Points B and C are chosen on these two lines such that AB=AC. Determine the possible equations of the line BC passing through the point (1,2).

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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58. Straight lines $3 x + 4 y = 5$ and $4 x - 3 y = 15$ intersect at the point $A$ . Points $B$ and $C$ are chosen on these two lines such that $A B = A C$ . Determine the possible equations of the line $B C$ passing through the point $(1, 2)$ .