Length of segment AB = [tex]8\sqrt{2}\ units[/tex]
Mid-point of segment AB = (0,2)
Step-by-step explanation:
Given points are:
A(-4,-2) = (x1,y1)
B(4,6) = (x2,y2)
Length of AB:
The distance formula will be used to calculate the length of segment AB:
[tex]d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Putting values
[tex]AB = \sqrt{(4-(-4))^2+(6-(-2)}\\= \sqrt{(4+4)^2+(6+2)^2}\\=\sqrt{(8)^2+(8)^2}\\=\sqrt{64+64}\\=\sqrt{132}\\=\sqrt{64*2}\\=\sqrt{8^2*2}\\=8\sqrt{2}[/tex]
Mid-point of AB:
Mid-point is given by the formula:
[tex]M = (\frac{x_1+x_2}{2} , \frac{y_1+y_2}{2})\\=(\frac{-4+4}{2} , \frac{-2+6}{2})\\=(\frac{0}{2} , \frac{4}{2})\\= (0,2)[/tex]
Hence,
Length of segment AB = [tex]8\sqrt{2}\ units[/tex]
Mid-point of segment AB = (0,2)
Keywords: Coordinate geometry. mid-point
Learn more about coordinate geometry at:
- brainly.com/question/4786449
- brainly.com/question/4793866
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