Distance between two points
Initial explanation: Pythagorean Theorem
If we have a right triangle:
by the Pythagorean Theorem, we know that:
a² + b² = hypotenuse²
Finding the distance between points
Step 1: locating the points M(2,7) and N(-3,1)
We know that the coordinates of a point indicate us its location in the x axis (the horizontal axis, left or right) and in the y axis (the veritcal axis, up or down) of the plane.
(x, y):
The first number (before the comma) shows its location on the x axis.
The second number (after the comma) shows its location on the y axis.
For M(2, 7), the point is located at x = 2 and y = 7
We locate each given point M and N:
Step 2: triangle
We want to find the distance from the points we draw (the purple line):
We can draw right triangle here:
Counting the measurements of the sides of the triangle: a and b, we have
a = 5
b = 6
Step 3: finding the distance
We can use the Pythagorean Theorem to find the distance, which is the hypotenuse of the right triangle we draw at the begining:
a² + b² = hypotenuse²
↓
5² + 6² = distance²
↓ since 5² = 25 and 6² = 36
25 + 36 = distance²
61 = distance²
↓ squaring root each side of the equation
√61 = √distance²
↓ since √distance² = distance
√61 = distance
Then, the distance is √61. Using a calculator we have that:
√61 = 7.8
Answer: 4) 7.8