Question

1. Find the length (distance) of segments AB, CD, and EF.

AB =

CD =

EF =
2. Find the midpoint of segments AB, CD, and EF.

AB =

CD =

EF =

3. Find the slope of the segments AB, CD, and EF.

AB =

CD =

EF =

Answer 1

1. AB = 7 units
CD= 3 units
EF= 5 units
2.AB= (-0.5, 2)
CD= (-4,-2.5)
EF=(2.5,-3)
3.AB=0
CD=undefined
EF=-4/3

Answer 2

1) AB=7 CD=3 EF=
`3√(5)` 2)
`M_(AB)=(-1)/(2),2`
`\\  M_(EF) =((5)/(2)-3)` \\
`\\ M_(EF) =((5)/(2)-3)` 3) AB not inclined CD not inclined EF 6/5

Explanation:

1) We can use the Distance Formula to answer the 1st. question.

But in the first case AB I'd rather doing it intuitively because it is a straight line parallel to the x-axis

AB

A(-4,2) and B(3,2)

In this segment, also parallel we can calculate the length as |-4|+|3|=7 since both have the same y coordinate.

Using the Distance formula to check it:

`D=\sqrt{(3--4)^(2)+(2-2)^(2)}\\D=√(49)\\D=7`

CD

C(-4,-1) D(-4,-4)

Similar to the first one but this time with different y coordinates.

The length will be calculated by subtracting the absolute values for y:

|-4|-|-1|=4-1 = 3

Using the Distance formula to check it:

`D=\sqrt{(-4--1)^(2)+(-4--4)^(2)}\\D=√(9)\\D=3`

EF

E (1,-1) F(4,-5)

In this case there's no straight line.

So right to the Distance Formula:

`D=\sqrt{(-5-1)^(2)+(4-1)^(2)}\\ D=√(36+9)\\D=√(45)\\D=3√(5)`

2) To find the Midpoints we need to calculate the Mean of these two points.

AB

A(-4,2) and B(3,2)

`M_(AB) =(-4+3)/(2),(2+2)/(2)\\M_(AB)=(-1)/(2),2`

CD

C(-4,-1) D(-4,-4)

`M_(CD) =(-4-4)/(2) ,(-1-4)/(2) \\M_(CD) =(0,(-5)/(2))`

EF

E (1,-1) F(4,-5)

`M_(EF) =(4+1)/(2) ,(-1-5)/(2) \\ M_(EF) =((5)/(2)-3)`

3) To find the Slope let's calculate the quotient of a difference between y-coordinates over x-coordinates of two given points.

`m_(AB)=(2-2)/(3--4)=(0)/(7)=0`

AB is not inclined.

CD

C(-4,-1) D(-4,-4)

`m_(CD)=(-4--1)/(-4--4)=(-3)/(-4+4)=(-3)/(0)`

Not Defined for all Real Set of Numbers

The line CD is not inclined.

EF

E(1,-1) F(4,-5)

`m_(EF)=(-5-1)/(4--1)=(6)/(5)`

The line EF has a slope of 6/5