Question

If three points A,B,C are collinear, then which of the following is true
a.AB + BC > AC
b.AB + BC = AC
c.AB + BC ≠ AC
d.AB + BC < AC​

Answer 1

Question: If three points A, B and C are Collinear, then which of the following is true?

AB + BC > AC

AB + BC = AC

AB + BC ≠ AC

AB + BC < AC

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AnswEr : If three given Points A, B and C are Collinear, then 'AB + BC = AC'. Option ( b ) is correct.

Collinear Points are the points which lie on a same line.

Non – Collinear Points are the points which do not lie on a same line.

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✇ If we've to find the Collinear Points then there are three Formulas to find out the Collinear Points which are Given by —

⠀⠀( I ) Distance Formula

⠀⠀( II ) Area of Triangle

⠀⠀( III ) Slope Formula

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❍ Basically, Distance Formula is used to find the distance b/w any two given Points:

$\sf{\sqrt{\Big\{x_2 - x_1\Big\}^2 + \Big\{y_2 - y_1\Big\}^2}} </p><p>{x </p><p>2</p><p> </p><p> −x </p><p>1</p><p> </p><p> } </p><p>2</p><p> +{y </p><p>2</p><p> </p><p> −y </p><p>1</p><p> </p><p> } </p><p>2$

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❍ Area of Triangle, when the area of Triangle formed by three point is Zero. Formula:

$\sf{\dfrac{1}{2} \Bigg[x_1(y_2 - y_3) +x_2(y_3 - y_1) + x_3(y_1 - y_2)\Bigg]} </p><p>2</p><p>1</p><p> </p><p> [x </p><p>1</p><p> </p><p> (y </p><p>2</p><p> </p><p> −y </p><p>3</p><p> </p><p> )+x </p><p>2</p><p> </p><p> (y </p><p>3</p><p> </p><p> −y </p><p>1</p><p> </p><p> )+x </p><p>3</p><p> </p><p> (y </p><p>1</p><p> </p><p> −y </p><p>2</p><p> </p><p> )]$

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❍ Slope formula measures the line segment step by step, formula:

$\sf{Q = \Bigg(\dfrac{y_2 - y_1}{x_2 - x_1}\Bigg)}Q=( </p><p>x </p><p>2</p><p> </p><p> −x </p><p>1</p><p> </p><p> </p><p>y </p><p>2</p><p> </p><p> −y </p><p>1</p><p> </p><p> </p><p> </p><p> )$

Answer 2

Answer:

Option (b) is true.

Step-by-step explanation:

Collinear points: The points which lie on the single straight line is known as collinear points.

Let A, B and C are three collinear points such that point B lies between A and C.

a. From figure,

Length of AC = Length of AB + Length BC

i.e., AB + BC = AC

Hence AB + BC > AC is not possible.

Thus, option (a) is false.

b. From figure,

Length of AC = Length of AB + Length BC

i.e., AB + BC = AC

Thus, option (b) is true.

c. Again by the same argument,

Length of AC = Length of AB + Length BC

i.e., AB + BC = AC

Hence AB + BC ≠ AC is not possible.

Thus, option (c) is false.

d. Clearly,

Length of AC = Length of AB + Length BC

i.e., AB + BC = AC

Hence AB + BC < AC is not possible.

Thus, option (d) is false.

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