The coordinates of the endpoints of AB are A(3,6) and B(7,–10). Point C is on AB and divides it such that AC:BC is 1:3. What are the coordinates of C?

1. Point P is on segment AB such that AP: PB is 2:5. If A has coordinates (-8, -2) and B has coordinates (6, 19), determine and state the coordinates of P.

P is 2/5 of the way from A to B.    

compute the distance from the x-coordinate of B to the x coordinate of A = 6--8 = 14.  

Multiply by 2/5 = 5.6.  And add that to the x-coordinate of A = 5.6 + -8 = -2.4

compute the distance from the y-coordinate of B to the y coordinate of A = 19--2 = 21.  

Multiply by 2/5 = 8.4.  And add to the y-coordinate of A = 8.4 + -2 = 6.4.  

Coordinates of P are (-4.4,6.4)

2. Point P is on segment AB such that AP: PB is 1:3. If A has coordinates (-3, -4) and B has coordinates (5, 0), determine and state the coordinates of P.

P is 1/4 of the way from A to B.  

compute the distance from the x-coordinate of B to the x coordinate of A = 5--3 = 8.  

Multiply by 1/4 = 2. And add that to the x-coordinate of A = 2 + -3 = -1

compute the distance from the y-coordinate of B to the y coordinate of A = 0--4 = 4.  

Multiply by 1/4 = 1. And add to the y-coordinate of A = 1 + -4 = -3.  

Coordinates of P are (-1,3)

3. Line v has an equation of y = –3/8 x + 5. Perpendicular to line v is line w, which passes through the point (6, 6). What is the equation of line w?

slope of line v is -3/8.  slope of line w is negative reciprocal of slope of line v = 8/3

y = 8/3x + b.  Plug in (6,6) for (x,y) in that equation to solve for b:

6 = 8/3(6) + b

b= -10

y = 8/3x -10

4. Line a has an equation of y = –1/3 x + 6. Line b includes the point (–1, 2) and is parallel to line a. What is the equation of line b?

slope of line a = -1/3.  slope of line b parallel to line a is identical = -1/3

y = -1/3x + b.  Plug in (-1,2) for (x,y) in that equation to solve for b:

2 = -1/3(-1) + b

5/3 = b

y = -1/3x + 5/3

5. The coordinates of the endpoints of AB are A(3,6) and B(7,–10). Point C is on AB and divides it such that AC:BC is 1:3. What are the coordinates of C?

Follow procedure done for 2nd problem which also has segments in ratio 1:3

Step-by-step explanation: