Solution 4.1:4a

From Förberedande kurs i matematik 1

If we draw in the points in a coordinate system, we can see the line between the points as the hypotenuse in an imaginary right-angled triangle, where the opposite and adjacent are parallel with the x- and y-axes, respectively.

In this triangle, it is easy to measure the lengths of the opposite and the adjacent, which are simply the distances between the points in the x- and y-directions, respectively.

∆x = 5 - 1 = 4  and  ∆y = 4 - 1 = 3

Using the Pythagorean theorem, we can then calculate the length of the hypotenuse, which is also the distance between the points:

d=(x)2+(y)2=42+32=16+9=25=5.

Note: In general, the distance between two points (xy) and (ab) is given by the formula

d=(x−a)2+(y−b)2.