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The points A(7, 8), B(-5, 2) and C(3, 6)

Question

The points $A (7, 8), B (- 5, 2)$ and $C (3, 6)$

are not collinear

cannot be plotted

are not defined

are collinear

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Luna Discussed

The points

A (7, 8), B (- 5, 2)

and

C (3, 6)

10 mins ago

Discuss this question LIVE

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Text solutionVerified

The given points are

A (x_{1}, y_{1}) = (7, 8), B (x_{2}, y_{2}) = (- 5, 2)

and

C (x_{3}, y_{3}) = (3, 6)

Now if

3

points

A (x_{1}, y_{1}), B (x_{2}, y_{2})

and

C (x_{3}, y_{3})

are collinear, then slope

m_{A B} = s l o p e m_{BC} =

slope

m_{A C}

Slope

m_{A B} = \frac{y _{2} - y _{1}}{x _{2} - x _{1}} = \frac{2 - 8}{- 5 - 7} = \frac{1}{2}

Slope

m_{BC} = \frac{y _{3} - y _{2}}{x _{3} - x _{2}} = \frac{6 - 2}{3 + 5} = \frac{1}{2}

and slope

m_{A C} = \frac{y _{3} - y _{1}}{x _{3} - x _{1}} = \frac{6 - 8}{3 - 7} = \frac{1}{2}

Therefore, slope

m_{A B} =

slope

m_{BC}

=

slope

m_{A C}

Therefore, the points

A, B

and

C

are collinear.

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Question Text	The points $A (7, 8), B (- 5, 2)$ and $C (3, 6)$
Answer Type	Text solution:1
Upvotes	150

The points A(7,8),B(−5,2) and C(3,6)

Text solutionVerified

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The points $A (7, 8), B (- 5, 2)$ and $C (3, 6)$