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Show that the following points are collinear. A(-5, 1), B(5, 5

Question

Show that the following points are collinear.
$A (- 5, 1), B (5, 5)$ and $C (10, 7)$ .

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Show that the following points are collinear.

A (- 5, 1), B (5, 5)

and

C (10, 7)

9 mins ago

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Text solutionVerified

Points are collinear if the area of a triangle is equal to zero.

Area of

Δ A BC = \frac{1}{2} [x_{1} (y_{2} - y_{3}) + x_{2} (y_{3} - y_{1}) + x_{3} (y_{1} - y_{2})]

A (- 5, 1), B (5, 5)

and

C (10, 7)

Δ = \frac{1}{2} {5 - (5 - 7) + 5 (7 - 1) + 10 (1 - 5)}

Δ = \frac{1}{2} {10 + 30 - 40}

Δ = 0

Hence points are collinear.

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Question Text	Show that the following points are collinear. $A (- 5, 1), B (5, 5)$ and $C (10, 7)$ .
Answer Type	Text solution:1
Upvotes	150