Find the value of "a" if the points are the indicated distances apart. (2,a) and (-3,-2) when d = the square root of 34

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You shoud remember the formula of distance between two points:

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

Replacing the distance and coordinates by the given values yields:

`sqrt34 = sqrt((2-(-3))^2 + (a-(-2))^2)`

`sqrt34 = sqrt(25 + (a+2)^2)`

Raising to square both sides yields:

`34 = 25 + (a+2)^2`

Subtracting 25 both sides yields:

`(a+2)^2 = 34-25 =gt (a+2)^2 =9 =gt a+2 = +-sqrt9 =gt a+2 = +-3`

Consider a+2 = 3 => a = 3-2 => a = 1

Consider a+2 = -3 => a = -3-2 => a = -5

**The coordinate `a` may have two values: `a=1` and `a=-5` .**

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