From the given figure
There is a line with 2 endpoints (4, 5) and (-3, -3)
We need to find the two sides of the right triangle formed from the line and the vertical, horizontal lines
The vertical side = 8 squares
The horizontal line = 7 squares
Then the 2 legs of the triangle are 8 and 7
We will use the Pythagorean relation to find the length of the line (the hypotenuse of the triangle)
[tex]h=\sqrt[]{(l_1)^2+(l_2)^2}[/tex]
Let l1 = 8 and l2 = 7, then
[tex]\begin{gathered} h=\sqrt[]{(8)^2+(7)^2} \\ h=\sqrt[]{64+49} \\ h=\sqrt[]{113} \end{gathered}[/tex]
The distance between the two given points is
[tex]\sqrt[]{113}[/tex]
