Pythagorean theorem?

Question

How do I use the pythagorean theorem to solve the following

I have two points on a graph

(1,1) and (3,2)

How do I determine the length of the line on the graph


I am also having trouble with a completly different equation, how do I find the distance between the following pair of points
(-3,0) and (4,0) . Do I use the pythagorean theorem here ....????

Answer 1

PROBLEM 1:

The horizontal distance is the difference in the x coordinates. The vertical distance is the difference in the y coordinates.

These two distances form the legs of a right triangle (a and b), and from there you can figure the length of the hypotenuse (c) which is the same as the distance between the points.

For example, with the points (1, 1) and (3, 2) you have x1 = 1, y1 = 1, x2 = 3, y2 = 2

Subtracting the x coordinates: x2 - x1 = 3 - 1 = 2
Subtracting the y coordinates: y2 - y1 = 2 - 1 = 1

So by Pythagorean theorem:
a² + b² = c²
1² + 2² = c²
1 + 4 = c²
c² = 5
c = sqrt(5)

So the distance between the points is sqrt(5)

PROBLEM 2:

For the second question however, they are in the same line horizontally (y-coords are the same), so the distance is just the difference in x coordinates. 4 - (-3) = 4 + 3 = 7.

Answer 2

The fact of the concept became got here across on a Babylonian pill circa 1900-1600 B.C. in spite of if Pythagoras (c.560-c.480 B.C.) or somebody else from his college became the 1st to locate its evidence can't be claimed with any degree of credibility. Euclid's (c 3 hundred B.C.) components grant the 1st and, later, the generic reference in Geometry.

Answer 3

l^2=(3-1)^2+(2-1)^2=2^2+1^2=4+1=5
l=√5

no, since these points are on a horizontal line
the length is
|-3-4|=7

Answer 4

a2+b2=c2