Mathematics, 27.10.2019 00:43, destinycolley728

Write a coordinate proof to prove that in an isosceles right triangle, the segment from the vertex of the right angle to the midpoint of the hypotenuse is perpendicular to the hypotenuse

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Answers

In an isosceles right triangle, the segment from the vertex of the right angle to the midpoint of the hypotenuse is perpendicular to the hypotenuse is proved

Solution:

Let we have a isosceles right angle triangle with coordinate O(0,0),A(k,0),B(0,k).

Here OA = OB and AB is the hypotenuse of the isosceles right angle triangle and according to question, the coordinates of midpoint M of hypotenuse is (k/2,k/2).

Now we know that the Slope of vertex is

$\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=m_{1}$

$\frac{\frac{k}{2}-0}{\frac{k}{2}-0}=1$

m_1 = 1 --- eqn 1

Now for Slope of line AB,

$m_{2}=\frac{0-k}{k-0}=-1$

m_2 = -1 --- eqn 2

on multiplying eq 1 and 2 we get

$m_1 \times m_2 = -1$

Since slope of AB multiplied with slope of OM is equal to -1. That means line AB is perpendicular to line OM

Hence in an isosceles right triangle, the segment from the vertex of the right angle to the midpoint of the hypotenuse is perpendicular to the hypotenuse is proved

answered: Guest

the correct answer is 828.07

answered: Guest

step-by-step explanation:

i found the life tables for the year 2012.

life table of males at age 30. probability of dying between ages x and x+1

total population:

29–30 . . . . . . . . . . . . 0.001030

30–31 . . . . . . . . . . . . 0.001061

males:

29–30 . . . . . . . . . . . . 0.001420

30–31 . . . . . . . . . . . . 0.001448

white population

29–30 . . . . . . . . . . . . 0.001005

30–31 . . . . . . . . . . . . 0.001037

white males

29–30 . . . . . . . . . . . . 0.001372

30–31 . . . . . . . . . . . . 0.001399

non hispanic white population

29–30 . . . . . . . . . . . . 0.001083

30–31 . . . . . . . . . . . . 0.001116

non hispanic white males

29–30 . . . . . . . . . . . . 0.001477

30–31 . . . . . . . . . . . . 0.001503

jacob, non hispanic white male. 30 years old.

probability that jacob lives to be 30 years old.

since the given probabilities are probabilities of dying, i think we simply subtract it from 1 to get the probability of living. we will use the probability of non hispanic white male.

probability of living to be 30 y.o.

29 - 30 : 1 - 0.001477 = 0.998523

30 - 31 : 1 - 0.001503 = 0.998497

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Write a coordinate proof to prove that in an isosceles right triangle, the segment from the vertex o...