How do you find the value of a given the points (2,a), (2,3) with a distance of 10?

Question

1448 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-04-13T12:39:17

See the entire solution process below:

The formula for calculating the distance between two points is:

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

Substituting the values given in the problem for the distance and the points gives:

$10 = sqrt((color(red)(2) - color(blue)(2))^2 + (color(red)(3) - color(blue)(a))^2)$

We can now solve for $a$ :

$10 = sqrt(0^2 + (color(red)(3) - color(blue)(a))^2)$

$10 = sqrt(0 + (color(red)(3) - color(blue)(a))^2)$

$10 = sqrt((color(red)(3) - color(blue)(a))^2)$

Remember, taking the square root results in a positive and negative result:

$10 = +-(color(red)(3) - color(blue)(a))$

Solution 1)

$10 = +(color(red)(3) - color(blue)(a))$

$10 = color(red)(3) - color(blue)(a)$

$-3 + 10 = -3 + color(red)(3) - color(blue)(a)$

$7 = 0 - color(blue)(a)$

$7 = -color(blue)(a)$

$-1 * 7 = -1 * -color(blue)(a)$

$-7 = a$

$a = -7$

Solution 2)

$10 = -(color(red)(3) - color(blue)(a))$

$10 = -color(red)(3) + color(blue)(a)$

$3 + 10 = 3 - color(red)(3) + color(blue)(a)$

$13 = 0 + color(blue)(a)$

$13 = color(blue)(a)$

$a$ can equal either $-7$ or $13$