SATHEE: Straight Line and Pair of Straight Lines 2 Question 5

Straight Line and Pair of Straight Lines 2 Question 5

5. The vertices of a triangle are $A (- 1, - 7), B (5, 1)$ and $C (1, 4)$ . The equation of the bisector of the angle $A B C$ is… .

$(1993, 2 M)$

Analytical & Descriptive Questions

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Answer:

Correct Answer: 5. $7 y = x + 2$

Solution:

Equation of the line $A B$ is $y - 1 = \frac{1 - (- 7)}{5 - (- 1)} (x - 5)$

$\begin{aligned} \Rightarrow y - 1 = \frac{8}{6} (x - 5) \Rightarrow y - 1 = \frac{4}{3} (x - 5) \\ \Rightarrow 3 y - 3 = 4 x - 20 \\ \Rightarrow 3 y - 4 x + 17 = 0 \end{aligned}$

Equation of the line $B C$ is

$\begin{matrix} y - 4 = \frac{4 - 1}{1 - 5} (x - 1) \Rightarrow y - 4 = - \frac{3}{4} (x - 1) \\ \Rightarrow 4 y - 16 = - 3 x + 3 \Rightarrow 3 x + 4 y - 19 = 0 \end{matrix}$

Again, equation of the bisectors of the angles between two given lines $A B$ and $B C$ are

$\begin{aligned} \frac{3 y - 4 x + 17}{\sqrt{3^{2} + 4^{2}}} = \pm \frac{4 y + 3 x - 19}{\sqrt{4^{2} + 3^{2}}} \\ \Rightarrow 3 y - 4 x + 17 = \pm (4 y + 3 x - 19) \\ \Rightarrow 3 y - 4 x + 17 = 4 y + 3 x - 19 \\ and 3 y - 4 x + 17 = - (4 y + 3 x - 19) \\ \Rightarrow 36 = y + 7 x and 7 y - x = 2 \end{aligned}$

Out of these two, equation of the bisector of angle $A B C$ is

$7 y = x + 2 .$

Straight Line and Pair of Straight Lines 2 Question 5

5. The vertices of a triangle are $A (- 1, - 7), B (5, 1)$ and $C (1, 4)$ . The equation of the bisector of the angle $A B C$ is… .

Analytical & Descriptive Questions

Answer:

Engineering Preparation

Medical Preparation

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Syllabus

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Sample Mock Test

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Straight Line and Pair of Straight Lines 2 Question 5

5. The vertices of a triangle are A(−1,−7),B(5,1) and C(1,4). The equation of the bisector of the angle ABC is… .

Analytical & Descriptive Questions

Answer:

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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5. The vertices of a triangle are $A (- 1, - 7), B (5, 1)$ and $C (1, 4)$ . The equation of the bisector of the angle $A B C$ is… .