3 Let A be an ordered plane (i. e. a model of I1-I3, B1-B4)....

Name: 3 Let A be an ordered plane (i. e. a model of I1-I3, B1-B4). Let A, B, C be three non-collinear points of A. Prove that there exists a line which intersects the three lines AB, BC, and CA in three different points M, N, and P, respectively, such that A*B*M, B*C*N, and A*C*P hold.
Uploaded: 2022-06-03T19:35:22-08:00
Duration: 1 min 33 s
Channel: Amanda Chavez
Description: 3 Let A be an ordered plane (i. e. a model of I1-I3, B1-B4). Let A, B, C be three non-collinear points of A. Prove that there exists a line which intersects the three lines AB, BC, and CA in three different points M, N, and P, respectively, such that A*B*M, B*C*N, and A*C*P hold.

3 Let A be an ordered plane (i. e. a model of I1-I3, B1-B4). Let A, B, C be three non-collinear points of A. Prove that there exists a line which intersects the three lines AB, BC, and CA in three different points M, N, and P, respectively, such that A*B*M, B*C*N, and A*C*P hold.

COLLINEAR POINTS Three or more points are collinear if they all lie on the same line. Use the steps below to determine if 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.