Regents Exam Questions : Directed Line Segments

In the diagram below, AC has endpoints with coordinates A(–5,2) and C(4,–10). If B is a point on AC and AB:BC = 1:2, what are the coordinates of B?

• (–2,–2)

• (–1/2,–4)

• (0,–14/3)

• (1,–6)

The coordinates of the endpoints of SC are S(–7,3) and C(2,–6). If point M is on SC, what are the coordinates of M such that SM:MC is 1:2?

• (–4,0)

• (0,–4)

• (–1,–3)

• (–5/2,–2/2)

Point M divides AB so that AM:MB = 1:2. If A has coordinates (–1,–3) and B has coordinates (8,9), the coordinates of M are

• (2,1)

• (5/3,0)

• (5,5)

• (23/3,8)

The endpoints of directed line segment PQ have coordinates of P(–7,–5) and Q(5,3). What are the coordinates of point A, on PQ, that divide PQ into a ratio of 1:3?

• A(–1,–1)

• A(2,1)

• A(3,2)

• A(–4,–3)

Line segment APB has endpoints A(–5,4) and B(7,–4). What are the coordinates of P if AP:PB is in the ratio 1:3?

• (–2,2)

• (–1,1.3)

• (1,0)

• (4,–2)

The endpoints of AB are A(–5,3) and B(7,–5). Point P is on AB such that AP:PB = 3:1. What are the coordinates of point P?

• (–2,–3)

• (1,–1)

• (–2,1)

• (4,–3)

What are the coordinates of the point on the directed line segment from K(–5,–4) to L(5,1) that partitions the segment into a ratio of 3 to 2?

• (–3,–3)

• (–1,–2)

• (0,–3/2)

• (1,–1)

Point P is on the directed line segment from point X(–6,–2) to point Y(6,7) and divides the segment in the ratio 1:5. What are the coordinates of point P?

• (4, 5/2)

• (1/2, -4)

• (-4 1/2, 0)

• (-4, -1/2)

• (1,1)

• (7,3)

• (9.6,3.6)

• (6.4,2.8)

Line segment PQ has endpoints P(–5,1) and Q(5,6), and point R is on PQ. Determine and state the coordinates of R, such that PR:RQ = 2:3.

• R = (–1, 3)

• R = (0, 4)

• R = (1, 2)

• R = (–3, 2)