Question

Apply the Pythagorean Theorem to find the length between the two points. Round your answer to the nearest hundredth. (4,3) (-2, -1)

Answer 1

The Pythagorean theorem applies to right-angled triangles. In the context of a coordinate plane, we can use it to find the distance between two points by creating a right-angled triangle where the points are the ends of the hypotenuse.

Let's denote the two points as P1(x1, y1) = (4, 3) and P2(x2, y2) = (-2, -1).

The horizontal distance (along the x-axis) between these points is the difference in their x-coordinates:
| x2 - x1 | = | -2 - 4 | = |-6| = 6

The vertical distance (along the y-axis) between these points is the difference in their y-coordinates:
| y2 - y1 | = | -1 - 3 | = |-4| = 4

These distances are the lengths of the two legs of the right-angled triangle. We'll call the horizontal distance 'a' and the vertical distance 'b', and the distance between the two points is the hypotenuse, which we'll call 'c'.

According to the Pythagorean theorem:
a^2 + b^2 = c^2

Therefore:
(6)^2 + (4)^2 = c^2
36 + 16 = c^2
52 = c^2

To find c, we take the square root of both sides of the equation:
c = √52

Now, let's find the decimal approximation and round it to the nearest hundredth:
c ≈ √52 ≈ 7.21

So the distance between the points (4,3) and (-2, -1), rounded to the nearest hundredth, is approximately 7.21 units.