Please help me out ?

Prove that the points (a, -3a), (2a, a) and (0, -2a) form a scalene trqingle

Dmitry [639]

Answer:

See below.

Step-by-step explanation:

Remember that a scalene triangle has lengths of different values.

Therefore, we just need to find the length or distance from each point to the next. If the three distances we acquire are different, then we prove that the point do indeed form a scalene triangle.

Let's let A be (a, -3a), B be (2a, a), and C be (0, -2a).

So, let's find each of the side lengths using the distance formula:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2$

Side AB:

Let's let A:(a, -3a) be (x₁, y₁) and let's let B:(2a, a) be (x₂, y₂). Substitute this into our formula:

$d=\sqrt{(2a-a)^2+(a-(-3a))^2$

Subtract:

$d=\sqrt{(a)^2+(4a)^2$

Square:

$d=\sqrt{a^2+16a^2}$

Add:

$d=\sqrt{17a^2}$

Simplify:

$d=\sqrt{a^2}\cdot \sqrt{17}\\d=|a|\sqrt{17}$

So:

$\overline {AB}=|a|\sqrt{17}$

Note: We need the absolute value because anything squared will be positive, and if you take the square root of something positive, the result will be positive. The absolute value ensures that the a value will be positive no matter what a is to begin with.

Side BC:

Let's let C:(0, -2a) be (x₁, y₁) and let's let B:(2a, a) be (x₂, y₂).

$d=\sqrt{(2a-0)^2+(a-(-2a)^2}$

Subtract:

$d=\sqrt{(2a)^2+(3a)^2}$

Square:

$d=\sqrt{4a^2+9a^2}$

Add:

$d=\sqrt{13a^2}$

Simplify:

$d=\sqrt{a^2}\cdot \sqrt{13}\\d=|a|\sqrt{13}$

Therefore:

$\overline{BC}=|a|\sqrt{13}$

Side AC:

Let's let A:(a, -3a) be (x₁, y₁) and let's let C:(0, -2a) be (x₂, y₂).

$d=\sqrt{(0-a)^2+(-2a-(-3a))^2$

Subtract:

$d=\sqrt{(-a)^2+(a)^2}$

Square:

$d=\sqrt{a^2+a^2}$

Add:

$d=\sqrt{2a^2}$

Simplify:

$d=|a|\sqrt2$

Therefore:

$\overline{AC}=|a|\sqrt2$

So, our three side lengths are:

$\overline {AB}=|a|\sqrt{17}\text{, }\overline{BC}=|a|\sqrt{13}\text{, and } \overline{AC}=|a|\sqrt2$

We can see that the three side lengths are different since they do not equal to same thing.

Therefore, we can deduce that the triangle must be scalene.

And we're done!

4 0

3 years ago

Read 2 more answers

10 divided by number e ?

djverab [1.8K]

Answer:

its 3.67679441171

Step-by-step explanation:

if you look at your calculator you can just type it in your welcome

8 0

3 years ago

Read 2 more answers

Find the greatest common factor

timama [110]

answers to 1 - 4:

1. GCF: 2

2. GCF: 3

3. GCF : 7

4. GCF: 3

4 0

3 years ago

The speed of a motorcycle increases from 10km/hr to 50km/hr in 9 seconds. What is its acceleration?

ivanzaharov [21]

Acceleration of motorcycle= 1.23m/s^2

Step-by-step explanation:

We need to find the acceleration of motorcycle When its speed increases from 10km/hr to 50km/hr in 9 seconds

Given:

Initial speed= 10km/hr

Final speed= 50km/hr

Time = 9 seconds

Acceleration = ?

Formula: $Acceleration =\frac{Change\,\,in\,\,velocity}{time}$

Solution:

We will first convert the speed from km/hr to m/s

Converting Initial speed 10km/hr into m/s

1 km = 1000 m

10 km = 10,000 m

and 1 hr = 3600 s

So, Initial speed = 10,000/3600 = 2.77 m/s

Converting Final speed 50km/hr into m/s

1 km = 1000 m

50 km = 50,000 m

and 1 hr = 3600 s

So, Initial speed = 50,000/3600 = 13.88 m/s

Now Using formula of acceleration:

$Acceleration =\frac{Change\,\,in\,\,velocity}{time}\\Change\,\,in\,\,velocity =Final\,\,speed-Initial\,\,speed\\Change\,\,in\,\,velocity=13.88 - 2.77\\Change\,\,in\,\,velocity = 11.11 m/s\\Acceleration =\frac{11.11}{9}\\Acceleration =1.23 m/s^2$

So, Acceleration of motorcycle = 1.23m/s^2

Keywords: Acceleration, Change in speed

Learn more about Acceleration at:

#learnwithBrainly

6 0

3 years ago

Could someone please help? What is the scale factor of the dilation shown?

aalyn [17]

Answer:

C: 3/4

Step-by-step explanation:

Hopefully this helps!

4 0

3 years ago