Exercises on three-point alignment condition

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Lined dots or collinear points they are points that belong to the same line.

Given three points ,  and , the condition of alignment between them is that the coordinates are proportional:

See a list of exercises on three-point alignment condition, all with full resolution.

Index

• Exercises on three-point alignment condition
• Resolution of question 1
• Resolution of question 2
• Resolution of question 3
• Resolution of question 4
• Resolution of question 5

Exercises on three-point alignment condition

Question 1. Check that the points (-4, -3), (-1, 1) and (2, 5) are aligned.

Question 2. Check that the points (-4, 5), (-3, 2) and (-2, -2) are aligned.

Question 3. Check if the points (-5, 3), (-3, 1) and (1, -4) belong to the same line.

Question 4. Determine the value of a so that the points (6, 4), (3, 2) and (a, -2) are collinear.

Question 5. Determine the value of b for the points (1, 4), (3, 1) and (5, b) that are vertices of any triangle.

Resolution of question 1

Points: (-4, -3), (-1, 1) and (2, 5).

We calculate the first side of the equality:

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We calculate the second side of the equality:

Since the results are equal (1 = 1), then the three points are aligned.

Resolution of question 2

Points: (-4, 5), (-3, 2) and (-2, -2).

We calculate the first side of the equality:

We calculate the second side of the equality:

How the results are different , so the three points are not aligned.

Resolution of question 3

Points: (-5, 3), (-3, 1) and (1, -4).

We calculate the first side of the equality:

We calculate the second side of the equality:

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How the results are different , so the three points are not aligned, so they do not belong to the same line.

Resolution of question 4

Points: (6, 4), (3, 2) and (a, -2)

Collinear points are aligned points. So we must get the value of a so that:

Substituting the coordinate values, we have to:

Applying the fundamental property of proportions (cross multiplication):

Resolution of question 5

Points: (1, 4), (3, 1) and (5, b).

The vertices of a triangle are unaligned points. So let's get the value of b to which the points are aligned and any other different value will result in non-aligned points.

Substituting the coordinate values, we have to:

Multiplying cross:

So for any value of b that is different from -2, we have the vertices of a triangle. For example, (1, 4), (3, 1) and (5, 3) form a triangle.

You may also be interested:

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