All categories

3 years ago

Find the area of the triangle with vertices: q(3,-4,-5), r(4,-1,-4), s(3,-5,-6).

Mathematics

1 answer:

maw [93]3 years ago

3 0

Answer:

(√6)/2 square units

Step-by-step explanation:

The area of a triangle is half the magnitude of the cross product of the vectors representing adjacent sides.

QR = (4-3, -1-(-4), -4-(-5)) = (1, 3, 1)

QS = (3 -3, -5-(-4), -6-(-5)) = (0, -1, -1)

The cross product is the determinant ...

$\text{det}\left|\begin{array}{ccc}i&j&k\\1&3&1\\0&-1&-1\end{array}\right|=-2i+j-k$

The magnitude of this is ...

|QR × QS| = √((-2)² +1² +(-1)²) = √6

The area of the triangle is half this value:

Area = (1/2)√6 . . . . square units

You might be interested in

A train is exactly 24km from Smalltown at 7:00p.m. It travels toward Smalltown at a constant rate of 90km per hour. At what time

N76 [4]

Answer:

7:16 P.M.

Step-by-step explanation:

24/90=4/15. There are 60 minutes in an hour, so we have 240/15=16.

5 0

3 years ago

What are the key aspects of the graph of f(x) = x2 – b2, where b is a real number?

netineya [11]

Given equation is $f\left(x\right)=x^2-b^2$ .

Now we need to find about what are the key aspects of the graph of $f\left(x\right)=x^2-b^2$ , where b is a real number.

We know that square of any number is always positive.

then $b^2$ must be a positive number.

So that means for any real number b, as the value of b increases then graph of f(x) shifts downward by $b^2$ units as compared to the graph of parent function $f\left(x\right)=x^2$

3 0

2 years ago

Read 2 more answers

Can anyone answer me pls I need help

Afina-wow [57]

Answer:

4,9

Step-by-step explanation:

i looked it up on a website,uhhhhh i don't know if its completely write soooo.....

8 0

2 years ago

Read 2 more answers

Which line segments are parallel in the diagram?

storchak [24]

The last option ,KH and LM

8 0

3 years ago

Read 2 more answers

Find the area of the regular polygon

Y_Kistochka [10]

Answer:

A = 374.123 ft^2

Step-by-step explanation:

First, lets calculate the perimeter:

Perimeter (p) = side length (s) * number of sides (n)

$p = s * n$

$p = 12 * 6$

$p = 72$

Next, lets find the apothem, which is the shortest length from any side to the middle. It's like the radius in a circle, but more complicated.

Apothem (a) = side length (s) / ( 2 * tan(180/number of sides (n)) )

$a = \frac{s}{2 * tan (\frac{180}{n} )}$

$a = \frac{12}{2 * tan (\frac{180}{6} )}$

$a = \frac{12}{2 * \frac{\sqrt{3} }{3}}$

$a = \frac{12}{\frac{2\sqrt{3} }{3}}$

$a = \frac{12*3}{2\sqrt{3}}$

$a = \frac{6*3}{\sqrt{3}}$

$a = \frac{18}{\sqrt{3}}$

Now, finally, to find the area of a regular polygon, we use the following equation:

Area (A) = ( apothem (a) * perimeter (p) ) / 2

$A = \frac{a * p}{2}$

$A = \frac{\frac{18}{\sqrt{3} } * 72}{2}$

$A = \frac{18}{\sqrt{3}} * 36$

$A = \frac{640}{\sqrt{3}}$

Turning into a decimal:

$A = 374.123 ft ^2$

8 0

2 years ago