# AHSA Geometry Questions; triangles and centers

*label*Mathematics

*timer*Asked: Jan 24th, 2019

*account_balance_wallet*$10

### Question Description

__I have included the rubric for these questions, so please follow the guidelines. I need clear and detailed work. I have included the page that these questions I mentioned are on, with the corresponding images that go with these tasks that are part of the question. Please make sure again, detailed work, and create images, graphs etc if applicable per question. Thank you very much!__

**Task 1 - ** Your math teacher manages a campground during summer vacation. He loves math so much that he has mapped the campground on a coordinate grid. Th e campsites have the following coordinates: Brighton Bluff at B(2, 2), Ponaganset Peak at P(4, 10), and Harmony Hill at H(12, 2). He wants to build showers that are equidistant from all three campsites. Find the coordinates of the point where the showers should be placed

**You can use proven theorems to explore relationships among sides, angles, and special lines and segments in triangles. **

**Task 2** -

** a. ** Draw nABC with obtuse /C and construct its orthocenter O. Then find the orthocenters of nABO, nACO, and nBCO. What did you discover? Explain why you get this result.

**b.** Will your conjecture be true for any acute or right nABC? Explain your reasoning

**You can use indirect reasoning to prove relationships within triangles. **

**Task 3 - ** In nABC, AB 2 BC. Show that there does not exist a point P on altitude BD that is equidistant from A and C.

## Tutor Answer

Attached you will find the outline and answers of your assignment. Please let me know if you need modifications or clarification.

5

To solve these

problems you

will pull together

many concepts

and skills

that you have

studied about

relationships

within triangles.

Pull It All Together

Coordinate Geometry

You can use the Midpoint Formula, the slope formula, and the relationship between

perpendicular lines to find points of concurrency.

Task 1

Your math teacher manages a campground during summer vacation. He loves math so

much that he has mapped the campground on a coordinate grid. The campsites have

the following coordinates: Brighton Bluff at B(2, 2), Ponaganset Peak at P(4, 10), and

Harmony Hill at H(12, 2). He wants to build showers that are equidistant from all three

campsites. Find the coordinates of the point where the showers should be placed.

Reasoning and Proof

You can use proven theorems to explore relationships among sides, angles, and special

lines and segments in triangles.

Task 2

a. Draw nABC with obtuse /C and construct its orthocenter O. Then find the

orthocenters of nABO, nACO, and nBCO. What did you discover? Explain why

y...

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