Mathematics, 21.07.2019 19:00 lyn94

Crater lake oregon is a roughly circular lake. the lake basin formed about 7000 years ago when the top of a volcano exploded in an immense explosion. hillman peak, garfield peak, and cloudcap are three mountain peaks on the rim of the lake. the peaks are located in a coordinate plane at h(-4,1), g(-2,-3), and c(5,-2). find the coordinates of the center of the lake.

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To solve the problem we must find the equation of the circumference of the form:
(Xa) ² + (Yb) ² = r²
They do not give us the center or the radio, but we have 3 points.
With the points H (-4,1), G (-2, -3) and C (5, -2) we find 3 equations
1) (-4-a) ² + (1-b) ² = r²
2) (-2-a) ² + (-3-b) ² = r ²
3) (5-a) ² + (-2-b) ² = r ²
Now we have a system of 3 equations with 3 unknowns: r, a, b
When solving the system we have to:
r = 5
a = 1
b = 1
Therefore, the center of the circumference of the lake is the point (a, b)
That is, the point (1,1)

Answer from: cw1242605

The coordinates of the center of the lake are $(\frac{-1}{3},\frac{-4}{3})$ .

Step-by-step explanation:

It is given that Hillman Peak, Garfield Peak, and Cloudcap are three mountain peaks on the rim of the lake. The peaks are located in a coordinate plane at H(-4,1), G(-2,-3), and C(5,-2).

If we joint these points, then we get a triangle and the center of a triangle is known as centroid.

The formula for centroid of a triangle is

$Centroid=(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3})$

The centroid of the triangle H(-4,1), G(-2,-3), and C(5,-2) is

$Centroid=(\frac{-4-2+5}{3},\frac{1-3-2}{3})$

$Centroid=(\frac{-1}{3},\frac{-4}{3})$

Therefore the coordinates of the center of the lake are $(\frac{-1}{3},\frac{-4}{3})$ .

Answer from: Quest

proofs involving isosceles triangles often require special consideration because an isosceles triangle has several distinct properties that do not apply to normal triangles.(more about triangle types) therefore, when you are trying to prove that two triangles are congruent, and one or both triangles, are isosceles you have a few theorems that you can use to make your life easier.

step-by-step explanation:

an isosceles triangle has two congruent sides and two congruent angles. the congruent angles are called the base angles and the other angle is known as the vertex angle. ∠bac and ∠bca are the base angles of the triangle picture on the left. the vertex angle is ∠abc

Answer from: Quest

3.64 deaths an hour.

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Crater lake oregon is a roughly circular lake. the lake basin formed about 7000 years ago when the t...

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