Find the equation of a line passing through the point of concurrence of medians of - ABC- and parallel AB where A-4- 3- B7- 1 and 0- 2

The correct option is A 2x + 11y = 24 Given Points #160; A( 4,3),B(7,1),C(0,2) Median of Δ ABC is ( x_1+x_2+x_33,y_1+y_2+y_33 ) Median is ...

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Byju's Answer

Standard XII

Mathematics

Point Slope Form of a Line

Find the equa...

Question

Find the equation of a line passing through the point of concurrence of medians of $Δ$ ABC, and parallel AB where $A (- 4, 3), B (7, 1)$ and $(0, 2)$

2 x + 11 y = 24

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x + y = 11

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2 x + y = 27

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x + 3 y = 15

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Solution

The correct option is A $2 x + 11 y = 24$
Given Points
$A (- 4, 3), B (7, 1), C (0, 2)$
Median of $Δ A B C$ is $(\frac{x_{1} + x_{2} + x_{3}}{3}, \frac{y_{1} + y_{2} + y_{3}}{3})$
Median is $(\frac{- 4 + 7 + 0}{3}, \frac{3 + 1 + 2}{3})$
Median is $(1, 2)$
Eq of line parallel to AB i.e. slope of line is equal to slope of AB
$m = m_{A B}$
$m = \frac{1 - 3}{7 + 4} = \frac{- 2}{11}$
Equation of line with slope m and point $(1, 2)$
$y - 2 = - \frac{2}{11} (x - 1)$
$11 y - 22 = - 2 x + 2$
$2 x + 11 y = 24$

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Find the equation of a line passing through the point of concurrence of medians of Δ ABC, and parallel AB where A(−4,3),B(7,1) and (0,2)

Find the equation of a line passing through the point of concurrence of medians of $Δ$ ABC, and parallel AB where $A (- 4, 3), B (7, 1)$ and $(0, 2)$