How do you find the value of a given the points (-5,3), (-3,a) with a distance of $sqrt5$ ?

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Answer 1 · 2017-02-03T14:50:20

$a=2$ or $a=4$

The distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by:

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

Therefore:

$sqrt(5) = sqrt((a - 3)^2 + (-3 - (-5))^2)$

Square both sides:

$(sqrt(5))^2 = (sqrt((a - 3)^2 + 4))^2$

$5 = (a - 3)^2 + 4$

$5 - 4 = (a- 3)^2$

$1 = (a - 3)^2$

Hence either $a-3=1$ i.e. $a=4$

or $a-3=-1$ i.e. $a=2$

Hopefully this helps!

How do you find the value of a given the points (-5,3), (-3,a) with a distance of sqrt5sqrt5?