- #1

nycmathguy

- Homework Statement:
- Collinear Points Discussion

- Relevant Equations:
- Lines & Collinear Points

Chapter 1, Section 1.1

Collinear Points

59. Three or more points are collinear

when they all lie on the same line. Use the steps below to determine whether the set of points {A(2, 3), B(2, 6),C(6, 3)} and the set of points {A(8, 3), B(5, 2), C(2, 1)} are collinear.

(a) For each set of points, use the Distance Formula to find the distances from A to B, from B to C, and from A to C. What relationship exists among these distances for each set of points?

(b) Plot each set of points in the Cartesian plane. Do all the points of either set appear to lie on the same line?

(c) Compare your conclusions from part (a) with the conclusions you made from the graphs in part (b). Make a general statement about how to use the Distance Formula to determine collinearity.

Let me see.

For (a), the Distance Formula must be used several times for each set.

Yes?

For (b), we simply plot each point on the xy-plane. We then see if the points are on the same line.

Yes?

For (c), you say? How do we use the Distance Formula to determine collinearity?

Collinear Points

59. Three or more points are collinear

when they all lie on the same line. Use the steps below to determine whether the set of points {A(2, 3), B(2, 6),C(6, 3)} and the set of points {A(8, 3), B(5, 2), C(2, 1)} are collinear.

(a) For each set of points, use the Distance Formula to find the distances from A to B, from B to C, and from A to C. What relationship exists among these distances for each set of points?

(b) Plot each set of points in the Cartesian plane. Do all the points of either set appear to lie on the same line?

(c) Compare your conclusions from part (a) with the conclusions you made from the graphs in part (b). Make a general statement about how to use the Distance Formula to determine collinearity.

Let me see.

For (a), the Distance Formula must be used several times for each set.

Yes?

For (b), we simply plot each point on the xy-plane. We then see if the points are on the same line.

Yes?

For (c), you say? How do we use the Distance Formula to determine collinearity?