How do you find a possible value for a if the points (-9,-2), (a, 5) has a distance of $d=7$ ?

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Answer 1 · 2017-03-18T00:45:48

See the entire solution process below:

The formula for calculating the distance between two points is:

$d = sqrt((color(red)(x_2) - color(blue)(x_1))^2 + (color(red)(y_2) - color(blue)(y_1))^2)$

Now, substitute $d$ and the values from the points given in the problem and solve for $a$ :

$7 = sqrt((color(red)(a) - color(blue)(-9))^2 + (color(red)(5) - color(blue)(-2))^2)$

$7 = sqrt((color(red)(a) + color(blue)(9))^2 + (color(red)(5) + color(blue)(2))^2)$

$7 = sqrt((color(red)(a) + color(blue)(9))^2 + (7)^2)$

$7 = sqrt((color(red)(a) + color(blue)(9))^2 + 49)$

$7^2 = (sqrt((color(red)(a) + color(blue)(9))^2 + 49))^2$

$49 = (color(red)(a) + color(blue)(9))^2 + 49$

$49 - color(red)(49) = (color(red)(a) + color(blue)(9))^2 + 49 - color(red)(49)$

$0 = (color(red)(a) + color(blue)(9))^2 + 0$

$0 = (color(red)(a) + color(blue)(9))^2$

$0 = (color(red)(a) + color(blue)(9))(color(red)(a) + color(blue)(9))$

We can now solve $a + 9$ for $0$ :

$a + 9 = 0$

$a + 9 - color(red)(9) = 0 - color(red)(9)$

$a + 0 = -9$

$a = -9$

$-9$ is a possible value for $a$ .

How do you find a possible value for a if the points (-9,-2), (a, 5) has a distance of d=7d=7?