Question

distances in the coordinate plane
sketch a right triangle between the points and determine the two side lengths.
what if the points are not along a grid line?
imagine if you create a right triangle from the points.
with a right triangle, you can calculate the distance between the two points with the pythagorean theorem. the distance between the two points is the hypotenuse.
$a^{2}+b^{2}=c^{2}$
to do this you simply need to count the distance offset between the two points horizontally (a) and vertically (b).
consider the points (3,2) and (9,10).
a=enter b=enter

Explanation:

Step1: Calculate horizontal side - length

Find the difference in x - coordinates. For points $(3,2)$ and $(9,10)$, the x - coordinates are 3 and 9. The horizontal side - length $a$ is $|9 - 3|$.
$a=|9 - 3|=6$

Step2: Calculate vertical side - length

Find the difference in y - coordinates. The y - coordinates are 2 and 10. The vertical side - length $b$ is $|10 - 2|$.
$b=|10 - 2| = 8$

Answer:

$a = 6$, $b = 8$