Question

Complete the sentence to finish the explanation of how you could show that points A, B, and C on the coordinate plane are collinear.

Answer 1

Answer:

• First blank: the equation of the line that passes through A and B

• Second blank: is a solution of the equation

Explanation:

Three or more points are collinear if and only if they are on the same line, and, thus they are solutions, of the same equation of the line.

When you know two points through their coordinates you can always find the equation of the line:

• Point A (x₁, y₁)

• Point B (x₂, y₂)

You can find the slope, m, of that line by using the slope formula:

• m = rise / run = Δy / Δx = (y₂ - y₁) / (x₂ - x₁)

And then, you apply the point-slope equation:

• y - y₁ =  m (x₂ - x₁)

Since you know m, x₁, and y₁, your equation is determined.

Once you have your equation, substitute the x and y coordinates with the coordinates of the point C. If, and only if, the equation is satisfied, the point C is on the same line and the three points are collinear.