Question

PLEASE ANYONE I NEED YOUR HELP. For the points A(-2, 10) and B(-4,6). Find each of the following.

a. AB
b. The coordinates of the midpoint of AB
c. The slope of AB​

Answer 1

a. _ √20 , about 4.472136

b - (-3, 8)

c- Slope of 2

Explanation:

Calculator

Answer 2

a.
`AB=2√(5)`

b.
`(-3,8)`

c.
`2`

Explanation:

You have the points:

A(-2,10)

where i will call:
`x_(1)=-2` and
`y_(1)=10`

B(-4,6)

where i will call:
`x_(2)=-4` and
`y_(2)=6`

for our calculations we are going to need the distance in x between the points (
`\Delta x` )and the distance in y between the points (
`\Delta y`):

`\Delta x =|x_(2)-x_(1)|=|-4-(-2)|=|-4+2|=|-2|=2\\\Delta y =|y_(2)-y_(1)|=|6-10|=|-4|=4`

a. To find AB (the distance between point A and point B) you need The Pythagorean Theorem:

`(AB)^2=(\Delta x)^2+(\Delta y)^2\\(AB)^2=(2)^2+(4)^2\\(AB)^2=4+16\\\\AB=√(20)\\ AB=2√(5)`

b. to find the coordinates of the midpoint we average the x-coordinates and the y coordinates

`x_(mid)=(x_(1)+x_(2))/(2) =(-2-4)/(2)=(-6)/(2) =-3\\y_(mid)=(y_(1)+y_(2))/(2) =(10+6)/(2)=(16)/(2) =8\\`

so the midpoint
`(x_(mid),y_(mid))` is at:
`(-3,8)`

c. For the slope we use the slope formula:

`slope=(y_(2)-y_(1))/(x_(2)-x_(1))=(6-10)/(-4-(-2))=(-4)/(-2)=2`

The slope is equal to 2.