First step to calculate the length of segment XY is to graph the points and link them with a line. Then draw two lines, one paralel to the x-axis and one paralel to the y-axis to form a right triangle below the segment.
Now following the graphic you can calculate the base (a) and height (b) of the triangle.
base a=Xy-Xx= 5-(-10)=5+10=15
height b=Yx-Yy= 2-(-5)=2+5=7
Havinf the base and height of the triangle you can apply the pythagoras theorem to calculate the length of the hypotenuse XY
[tex]\begin{gathered} a^2+b^2=c^2 \\ c^2=(15)^2+(7)^2 \\ c^2=274 \\ c=\sqrt{274}=16.55 \end{gathered}[/tex]
The length of segment XY=16.55
