Respuesta :
Answer:
a. _ √20 , about 4.472136
b - (-3, 8)
c- Slope of 2
Step-by-step explanation:
Calculator
Answer:
a. [tex]AB=2\sqrt{5}[/tex]
b. [tex](-3,8)[/tex]
c. [tex]2[/tex]
Step-by-step explanation:
You have the points:
A(-2,10)
where i will call: [tex]x_{1}=-2[/tex] and [tex]y_{1}=10[/tex]
B(-4,6)
where i will call: [tex]x_{2}=-4[/tex] and [tex]y_{2}=6[/tex]
for our calculations we are going to need the distance in x between the points ([tex]\Delta x[/tex] )and the distance in y between the points ([tex]\Delta y[/tex]):
[tex]\Delta x =|x_{2}-x_{1}|=|-4-(-2)|=|-4+2|=|-2|=2\\\Delta y =|y_{2}-y_{1}|=|6-10|=|-4|=4[/tex]
a. To find AB (the distance between point A and point B) you need The Pythagorean Theorem:
[tex](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}[/tex]
b. to find the coordinates of the midpoint we average the x-coordinates and the y coordinates
[tex]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\\[/tex]
so the midpoint [tex](x_{mid},y_{mid})[/tex] is at: [tex](-3,8)[/tex]
c. For the slope we use the slope formula:
[tex]slope=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{6-10}{-4-(-2)}=\frac{-4}{-2}=2[/tex]
The slope is equal to 2.
