Question 63760: I am currently taking elementary algebra and our instuctor gave us a handout w/3 questions on it. I had never even heard of Pythagorean anything and we have not discussed it in class. Please help me:
Show that the following 3 points form a right triangle. Use the distance formula & Pythagorean formula.
(-1.6, 3.8), (-6, -5), (-6, 6)
Answer by praseenakos@yahoo.com(507)   (Show Source):
You can put this solution on YOUR website! QUESTION:
Show that the following 3 points form a right triangle. Use the distance formula & Pythagorean formula.(-1.6, 3.8), (-6, -5), (-6, 6)
ANSWER;
Pythagoras was a Greek mathematician who lived about 2500 years ago, and who developed the most famous formula in geometry, possibly in all of mathematics!
He proved that, for a right triangle, the sum of the squares of the two sides that join at a right angle equals the square of the third side. The third side--the side opposite the right angle--is called the hypotenuse of the right triangle. The two shorter sides are usually called "legs."
This formula is called the Pythagorean Theorem in honor of Pythagoras. It is usually written as the equation below, where a and b are the measures of the legs of the triangle and c is the measure of the hypotenuse.
c^2 = a^2 + b^2
Let's try out the Pythagorean Theorem using this right triangle with sides of 5 and 12 cm, and a hypotenuse of 13 cm.
Here c = 13 (because, longest side)
a = 5
b = 12
We can verify that the Pythagorean Theorem is true by substituting in the values. The square root of 169 is 13, which is the measure of the hypotenuse in this triangle.
also 12^2 = 144
5^2 = 25
144 + 25 = 169
Now let's come back to your question.
Here coordinates of three points are given,.
(-1.6, 3.8), (-6, -5), (-6, 6)
Let's take them as,
A(-1.6, 3.8),
B (-6, -5),
C (-6, 6)
Using distance formula, we can find out the lenth of sides of the triangle,
( Draw a triangle ABC whose coordinates are .(-1.6, 3.8), (-6, -5), (-6, 6))
Distance formula,
d = square root of {difference bn x coordinates)^2 +(diff bn y coor)^2}
so,
AB = square root of {-1.6 - (-6))^2 +(3.8 - (-5)^2}
= square root of {4.4)^2 +(8.8)^2}
= square root of {19.36 + 77.44
= square root of (97.30)
(AB)^2 =97.3
(BC)^2 = square root of {difference bn x coordinates)^2 +(diff bn y coor)^2}
= square root of {-6-(-6))^2 +(-5-(6))^2}
= square root of {0)^2 +(-11)^2}
= square root of {0 + 121
= square root of 121
==> BC^2 = 121
Similarly, AC^2 = (-1.6 -( -6) )^2 + ( 3.8 -6 ) ^2
= (4.4)^2 + (2.2)^2
= 19.36 + 4.84
AC^2 = 24.20
Now here we have
BC^2 = 121
(AB)^2 =97.3
AC^2 = 24.20
So we can write it as ,
BC^2 = AB^2 + AC^2
That means, the sides satisfies pythagorean theorem.
That means the given points forms a right triangle.
Hope you understood.
Regards.
praseenakos@yahoo.co.in
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