Question

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

Answer 1

Answer:

a. _ √20 , about 4.472136

b - (-3, 8)

c- Slope of 2

Step-by-step explanation:

Calculator

Answer 2

Answer:

a. $AB=2\sqrt{5}$

b. $(-3,8)$

c. $2$

Step-by-step 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:

$(AB)^2=(\Delta x)^2+(\Delta y)^2\\(AB)^2=(2)^2+(4)^2\\(AB)^2=4+16\\\\AB=\sqrt{20}\\ AB=2\sqrt{5}$

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

$x_{mid}=\frac{x_{1}+x_{2}}{2} =\frac{-2-4}{2}=\frac{-6}{2} =-3\\y_{mid}=\frac{y_{1}+y_{2}}{2} =\frac{10+6}{2}=\frac{16}{2} =8$

so the midpoint $(x_{mid},y_{mid})$ is at: $(-3,8)$

c. For the slope we use the slope formula:

$slope=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{6-10}{-4-(-2)}=\frac{-4}{-2}=2$

The slope is equal to 2.