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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:

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.

**To download this list of exercises on three-point alignment condition, click here!**

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