Consider the points a(3,−3), b(−2, 1), c(6, 0), and d(1, 4). point a is joined to point b to create segment ab and point c is joined to point d to create segment cd.
part a
a. what is the slope of ab?
b. what is the slope of cd?

segments ab and cd are translated 2 units to the left to get segments a′b′ and c′d′.
part b
a. what is the slope of a′b′?
b. what is the slope of c′d′?

Part A:

a. The slope of AB is

b. The slope of CD is

Part B:

a. The slope of A'B' is

b. The slope of C'D' is

Step-by-step explanation:

- The rule of a slope of a line whose endpoints are

  and is

Part A:

∵ Point A = (3 , -3) and point B = (-2 , 1)

∵ Point C = (6 , 0) and point D = (1 , 4)

a.

∴

∴ The slope of AB is

b.

∴

∴ The slope of CD is

- The image of point (x , y) by translation to the left k units is (x - k , y)

- Translation doesn't change the slope of a line, so the line and its

  image have same slope

Part B:

∵ Segments AB and CD are translated 2 units to the left to get

   segments A′B′ and C′D′

∵ Point A' = (3 - 2 , -3) and point B' = (-2 - 2 , 1)

∴ Point A' = (1 , -3) and point B' = (-4 , 1)

∵ Point C' = (6 - 2 , 0) and point D' = (1 - 2 , 4)

∴ Point C' = (4 , 0) and point D' = (-1 , 4)

a.

∴

∴ The slope of A'B' is

b.

∴

∴ The slope of C'D' is

answer: all the values are within because it has a pattern that repeats from -6 to 4.

good luck!