Between the points (-2,7) and (-7,-5) find:

a) The Distance

b) The Midpoint

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a) To calculate the distance d between two points` (x_1,y_1)` and `(x_2,y_2)` use the formula:

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

Here,` x_1=-2, x_2=-7, y_1=7 and y_2=-5.`

So, d`=sqrt({-7-(-2)}^2+(-5-7)^2)`

` =sqrt((-5)^2+(-12)^2)`

` =sqrt(25+144)`

` =sqrt169`

=13 units.

**Therefore, the distance between the points (-2,7) and (-7,-5) is 13 units.**

b) To find the mid point between the two points `(x_1,y_1)` and `(x_2,y_2)` use the formula:

Mid point=`((x_1+x_2)/2,(y_1+y_2)/2)`

Here, `x_1=-2, x_2=-7, y_1=7 and y_2=-5` . Now, plug in the values in the above formula.

Mid point=`((-2+(-7))/2,(7+(-5))/2)`

=`(-9/2,2/2)`

=`(-4.5,1)`

**Therefore, the mid point between the points (-2,7) and (-7,-5) is `(-4.5,1)` .**

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