Explain how you could use the Pythagorean Theorem to find the distance between the points the coordinate pair negative four comma negative three and the coordinate pair one comma one. Find the distance. You can type carat two to indicate "squared" and "sqrt" to indicate "square root." (Examples: five carat two equals five squared and sqrtsqrt twenty-five equals the square root of twenty-five)
It is easier to read and understand your prob. in mathematical form.
(-4,-3), (1,1).
d^2 = X^2 + y^2,
d^2 = (x2-x1)^2 + (y2-y1)^2,
d^2 = (1-(-4))^2 + (1-(-3))^2,
d^2 = (1+4)^2 + (1+3)^2,
d^2 = 5^2 + 4^2,
d^2 = 25 + 16 = 41,
d = sqrt41 = 6.40.
Some of the steps can be omitted when you learn the operation.
chicken butt
i RULE!!!!!!!!!!!!!!!!!!!!
, the author's not a eexrpt mathematician (in fact, he's a graphics designer who appears to be working in video games), so he may have never tried going through an explanation of Euler's formula to find out that it's not magic. I only did so myself with the help of a video lecture by Edward Burger that I found on one of his DVD courses on mathematics for The Learning Company: Burger is generally extremely clear and a good resource if you can find his stuff in your library as I did. Not sure what's available on YouTube, etc. to unpack that particular bit of mathematical magic. However, it shouldn't come as TOO much of a shock to anyone who knows at least enough about complex numbers to know that multiplying a vector by i gives a 90 counterclockwise rotation on the complex plane.All that said, the use of color in formulas seems like a great way to organize one's own thinking about what's going on as well as to do presentations to others. Might be a very nice thing to have students do for themselves/each other when they explain their ideas and problem solutions. Kids do like color and coloring, I can say that for sure based on one of the most successful units I've ever taught to alternative education students back in 1999-2000: graph coloring. Students who'd never done squat in my classes suddenly were writing A exams and enjoying themselves. Too bad I didn't figure that out a lot sooner.
To find the distance between two points using the Pythagorean Theorem, we need to remember that it applies to right-angled triangles. In this case, we can consider the line connecting the two points as the hypotenuse of a right triangle.
The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the square of the lengths of the other two sides (a and b). Mathematically, it can be represented as:
c^2 = a^2 + b^2
Now, let's apply this to the given coordinates.
The first coordinate pair is (-4, -3), which we can label as point A. The second coordinate pair is (1, 1), labeled as point B.
To find the distance, we need to calculate the length of the hypotenuse, which will be the distance between these two points.
First, we find the length of the horizontal side (a), which can be calculated as the difference between the x-coordinates of the two points: a = (1 - (-4)) = 5.
Next, we find the length of the vertical side (b), calculated as the difference between the y-coordinates of the two points: b = (1 - (-3)) = 4.
Now that we have the values for the sides of the right triangle, we can use the Pythagorean Theorem to find the distance (c):
c^2 = a^2 + b^2
c^2 = 5^2 + 4^2
c^2 = 25 + 16
c^2 = 41
To find the distance, we need to take the square root of both sides of the equation:
c = sqrt(41)
Therefore, the distance between the two points is sqrt(41).