Question

Find the length of segment GH with endpoints G(5, -9) and H(-6, -7)

(Show work)

Answer 1

Answer:

5√5

For explanation, refer the attachment

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Answer 2

Given:

• A line segment GH with endpoints as G (5, -9) and H (-6, -7)

To find:

• Length of Line segment GH =?

Formula required:

• Distance formula

$\purple{\bigstar}\boxed{\sf{Distance\:\:AB=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2\;}}}$

[ Where $\sf{(x_1,y_1)}$ and $\sf{(x_2,y_2)}$ are coordinates of points A and B respectively ]

Solution:

On comparing we will get

• $\sf{x_1=5\;;\;y_1=-9}$

• $\sf{x_2=-6\;;\;y_2=-7}$

Using Distance formula

$\implies\sf{GH=\sqrt{(5-(-6))^2 + (-9-(-7))^2\;}}$

$\implies\sf{GH=\sqrt{(5+6)^2 + (-9+7)^2\;}}$

$\implies\sf{GH=\sqrt{121+ 4\;}}$

$\implies\sf{GH=\sqrt{125\;}}$

$\implies\boxed{\boxed{\sf{GH=5\sqrt{5}\;\;units}}}\purple{\bigstar}$

Therefore,

• Length of Line segment GH would be 5√5 units.