Answer:
The Pythagorean Theorem can be used to find the length of the legs and hypotenuse of a triangle. While the distance of a vertical or horizontal line can be counted easily, a diagonal line cannot be determined the same way. A diagonal line, such as the line between the two points shown on the graph, is the hypotenuse of an imaginary right triangle. If you draw the legs of the triangle by drawing straight lines through the points on the graph until the lines meet at a point, you can count the distance of the legs and plug those values into the Pythagorean Theorem.
Step-by-step explanation:
In this case, the meeting point of straight lines drawn through the points is
(-3, -4)
and the distances of the legs of the right triangle are 8 and 6. The theorem is
a² + b² = c²
so 8² + 6² = c² to 64 + 36 = c² to 100 = c² and [tex]\sqrt 100 = \sqrt c^{2}[/tex]
so 10 = c
The distance of the line (hypotenuse) is 10.
