Step-by-step explanation:
strange way of phrasing this.
if I understand correctly we have the points
(-4, 6) and (-1, 6).
the first number is the x coordinate, the second number the y coordinate.
but sure, you can write points also as vectors (the coordinate values on top of each other). they are then all pointers from the origin (0, 0) to the designated points.
anyway, once we understand the coordinates of the points, we see that both have the same y coordinate.
when 2 points have the same x or the same y coordinates it is easy to calculate the distance (at least in 2 dimensions) : it is simply the absolute value of the difference in the other coordinate.
in our case here : |-4 - -1| = |-4 + 1| = |-3| = 3
so, the distance between both points is 3.
if the points do not share a coordinate value, like for
(-4, 6) and (-1, 2), we need to use Pythagoras for right-angled triangles.
c² = a² + b²
c is the Hypotenuse (the baseline, the side opposite of the 90 degree angle) and would be the distance between the 2 points.
a and b are the other 2 sides (often called legs) on each side of the 90 degree angle. they would be the difference of the x coordinates and the difference of the y coordinates.
so, in my example,
c² = (-4 - -1)² + (6 - 2)² = (-3)² + 4² = 9 + 16 = 25
c = sqrt(25) = 5
the distance between these 2 points would therefore be 5.
please note that in this case we don't bother with the absolute value, because we are squaring the elements. and squaring always delivers a positive result.
