Help for the slope of this I get 2 and 1/3 but i need to get a negative reciprocal
(4,5),(8,13)(-4,9)
I need to show triangle ABC is a right triangle
2 1/3 = 7/3
so, the negative reciprocal is -3/7
surely you have outgrown using mixed numbers ...
Ah! I'll help.
When finding a reciprocal, you first need convert the mixed number into a improper fraction. (Improper fractions are fractions that have more parts than the whole, such as; 100/55 or 400/100)
To convert 2 1/3, we need to multiply the whole numbers by the denominator, and then add the numerator.
2*3 is 6, and 6+1 is 7. This leaves the improper fraction 7/3.
All a reciprocal is, is the numerator and denominator switched.
Therefore, 7/3's reciprocal is 3/7, and as a negative number, it is -3/7.
The Negative Reciprocal is -3/7! I hope this helps! Have an awesome day, and I wish you luck.
To find the slope of a line passing through two points, you can use the formula:
slope = (y2 - y1) / (x2 - x1)
Let's use this formula for the given points (4,5) and (8,13):
slope = (13 - 5) / (8 - 4)
slope = 8 / 4
slope = 2
The slope of the line passing through the points (4,5) and (8,13) is 2.
To find the negative reciprocal of a number, you simply take the reciprocal (which is 1 over the number) and then change the sign to the opposite.
In this case, the negative reciprocal of 2 would be:
negative reciprocal of 2 = -1/2
So, the negative reciprocal of the slope, which is 2, is -1/2.
Now, let's move on to proving that triangle ABC is a right triangle using the given points.
The given points are (4,5), (8,13), and (-4,9).
To determine if a triangle is a right triangle, we need to check if the sum of the squares of two sides is equal to the square of the third side.
Let's calculate the lengths of the sides and see if the condition holds true:
Side AB:
Length of AB = √[(x2 - x1)^2 + (y2 - y1)^2]
Length of AB = √[(8 - 4)^2 + (13 - 5)^2]
Length of AB = √[4^2 + 8^2]
Length of AB = √[16 + 64]
Length of AB = √80
Length of AB = 4√5
Side BC:
Length of BC = √[(x2 - x1)^2 + (y2 - y1)^2]
Length of BC = √[(-4 - 8)^2 + (9 - 13)^2]
Length of BC = √[(-12)^2 + (-4)^2]
Length of BC = √[144 + 16]
Length of BC = √160
Length of BC = 4√10
Side CA:
Length of CA = √[(x2 - x1)^2 + (y2 - y1)^2]
Length of CA = √[(4 - (-4))^2 + (5 - 9)^2]
Length of CA = √[8^2 + (-4)^2]
Length of CA = √[64 + 16]
Length of CA = √80
Length of CA = 4√5
Now, check if the Pythagorean theorem holds true for triangle ABC:
(Length of AB)^2 + (Length of BC)^2 = (Length of CA)^2
(4√5)^2 + (4√10)^2 = (4√5)^2
16 * 5 + 16 * 10 = 16 * 5
80 + 160 = 80
240 = 80
The Pythagorean theorem does not hold true for triangle ABC since the equation is not balanced.
Therefore, triangle ABC is not a right triangle based on the given points.