Question

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Answer 1

$\huge\bf\underline{\pink{Question:-}}$

Find the value of m if the points(5,1),(-2,-3),and (8,2m) are collinear then find the value of m.

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$\large\bf\underline{\blue{Answer}}$

m=19/4

$\large\bf\underline{\green{Given:-}}$

Three points are given as A(5,1) ,B(-2,-3) ,C(8,2m).

$\large\bf\underline{\green{To\:\:Find:-}}$

$\bf \:we\: need\: to\: find \:the \:Value \:of \:m.$

$\huge{\underline{\bf{\red{Solution:-}}}}$

If A B and C are collinear then ar ∆ABC = 0.

$\bf \: ar \triangle \: ABC=\\{\underline{\boxed{ = \frac{1}{2}[x_{1}( y_{2} - y_{3})+x_2(y_3-y_1)+x_3(y_1-y_2)}}}$

$:\implies$½[5(-3-2m)+(-2)(2m-1)+8(1-(-3)]

$:\implies$ ½[- 15 -10m -4m + 2 + 8 + 24 ] = 0

$:\implies$ ½[-15 -14m +34 ] = 0

$:\implies$ ½[19 -14m ] = 0

$:\implies$ [19 - 14m] = 0×2

$:\implies$ 19 = 14m

$:\implies$ m = 19/14

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Answer 2

Question :

Find the Value of m If the point ( 5 , 1 ) , ( -2 , -3 ) and ,( 8 , 2m ) are Collinear.

To Find :

The value of m.

Given :

• Point ( 5 , 1 )
• Point ( -2 , -3 )
• Point ( 8 , 2m )

Formula Required :

$\tt\dagger \: \: \: \: \: Area_\triangle = \dfrac{1}{2} [ x_1( y_2 - y_3 ) +x_2 ( y_3 - y_1) + x_3 ( y_1 + y_2) ]$

Solution :

Let Point be,

• A ( 5 , 1 )
• B ( -2 , -3 )
• C ( 8 , 2m )
• x1 = 5.
• x2 = -2.
• x3 = 8.
• y1 = 1.
• y2 = -3.
• y3 = 2m.

$\rule{90}1$

# If A B and C are Collinear then Area of ∆ ABC be equal to 0.

$\tt\longmapsto0 = \frac{1}{2} [5( - 3 - 2m) - 2(2m - 1) + 8(1 + 3)]$

$\tt\longmapsto0 = - 15 - 10m - 4m + 2 + 32.$

$\tt\longmapsto 0 =34 - 15 - 14m.$

$\tt\longmapsto \cancel{ - }19 = \cancel{ - } 14m.$

$\tt\longmapsto m = \dfrac{19}{14}$

Therefore, the value of m is 19/14.