Between the points (5,4) and (-5,-4) find:

a) The distance (Simplified radical)

b) The midpoint (use .5 for 1/2)

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a) The distance d between the points `(x_1,y_1)` and `(x_2,y_2)` in a plane is:

`d=sqrt((x_2-x_1)^2+(y_2-y_1)^2)`

So, the distance between the points `(5,4)` and `(-5,-4)` is:

`d=sqrt((-5-5)^2+(-4-4)^2)`

`=sqrt(100+64)`

`=sqrt164`

`=sqrt(2*2*41)`

`=2sqrt41` units.

b) The midpoint of the line segment joining the points `(x_1,y_1) ` and `(x_2,y_2)` is given by:

Midpoint=`(0.5(x_1+x_2), 0.5(y_1+y_2))`

So, the midpoint of those two points is at:

`(0.5(5+(-5)), 0.5(4+(-4)))`

`=(0.5*0,0.5*0)`

`=(0,0)`

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