# POC Scenario

### By Casie Wilford

## Which two should I go to?

Taffy is going to Comic con on Saturday and there are 3 of her favorite booths. Her best friend ate a bad churro and wants to go home. She only has time to go to ONE of the closest booths. CT is the altitude of the triangle below. Out of all 3 booths, which TWO will she not be able to visit?

## Extra Info

Each point: A,B, and C, are the booths , and T is where Taffy is.

## Step 1

First find the orthocenter of the triangle like in the picture above.

## Step 2

Extend lines and list points to point T, which is Taffy.

## Step 3

Find the slope of each line and put into the equation of lines.

## Step 4

Find each of the distances from T to the vertex and figure out which one is the smallest using the distance formula below.

## Intersetion

They all intersect at (0,0) which is where Taffy will be standing.

## Question

Now knowing what the lengths are from Taffy to each booth, which two will she not be able to visit?

## Answer

TC is the shortest so that means that B and A are the booths Taffy will not be able to visit.

## POC

Altitude seemed like it would be the best for this scenario. Being able to find distances from her to each vertex (booth). The altitude being a perpendicular bisector of AB and Taffy being the orthocenter where they all intersect. So being able to use this shows the point -or the orthocenter - where they all intersect at out side of the circle where Taffy is standing. Also that each point (A,B,C) are the booths and T is Taffy.