SATHEE: Straight Line and Pair of Straight Lines 1 Question 16

Straight Line and Pair of Straight Lines 1 Question 16

16. If the line $3 x + 4 y - 24 = 0$ intersects the $X$ -axis at the point $A$ and the $Y$ -axis at the point $B$ , then the incentre of the triangle $O A B$ , where $O$ is the origin, is

(2019 Main, 10 Jan I)

(a) $(4, 3)$

(b) $(3, 4)$

(d) $(2, 2)$

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Solution:

Given equation of line is

$3 x + 4 y - 24 = 0$

For intersection with $X$ -axis put $y = 0$

$\begin{aligned} \Rightarrow & 3 x - 24 & = 0 \\ \Rightarrow & x & = 8 \end{aligned}$

For intersection with $Y$ -axis, put $x = 0$

$\Rightarrow 4 y - 24 = 0 \Rightarrow y = 6$

$∴ A (8, 0)$ and $B (0, 6)$

Let $A B = c = \sqrt{8^{2} + 6^{2}} = 10$

$O B = a = 6$

and $O A = b = 8$

Also, let incentre is $(h k)$ , then

$\begin{aligned} h & = \frac{a x_{1} + b x_{2} + c x_{3}}{a + b + c} (here, x_{1} = 8, x_{2} = 0, x_{3} = 0) \\ = \frac{6 \times 8 + 8 \times 0 + 10 \times 0}{6 + 8 + 10} = \frac{48}{24} = 2 \end{aligned}$

and $k = \frac{a y_{1} + b y_{2} + c y_{3}}{a + b + c} ($ here, $y_{1} = 0, y_{2} = 6, y_{3} = 0)$

$= \frac{6 \times 0 + 8 \times 6 + 10 \times 0}{6 + 8 + 10} = \frac{48}{24} = 2$

$∴$ Incentre is $(2, 2)$ .

Straight Line and Pair of Straight Lines 1 Question 16

16. If the line $3 x + 4 y - 24 = 0$ intersects the $X$ -axis at the point $A$ and the $Y$ -axis at the point $B$ , then the incentre of the triangle $O A B$ , where $O$ is the origin, is

Solution:

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Straight Line and Pair of Straight Lines 1 Question 16

16. If the line 3x+4y−24=0 intersects the X-axis at the point A and the Y-axis at the point B, then the incentre of the triangle OAB, where O is the origin, is

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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16. If the line $3 x + 4 y - 24 = 0$ intersects the $X$ -axis at the point $A$ and the $Y$ -axis at the point $B$ , then the incentre of the triangle $O A B$ , where $O$ is the origin, is