Ms+Gravel's+Class+-+Group+1

=**"How To"...**= ===**Group 1:** Find the height of the triangle (length of the altitude) given 3 points. You may use the triangle A(-1,3), B(-2, -1), and C(2, 1) to demonstrate the concept with altitude going from point A. ===

We have 3 points to try and find the length of the altitude: A(-1,3), B(-2,-1), C(2,1)



Step 1: Find the equation of the altitude. Step 2: Find the equation of AC. Step 3: Find the POI of AC and the altitude. Step 4: Using the POI and B(where the altitude begins) to find the length of the altitude.

How to find the equation of the altitude:

1. Find the slope of AC

M = __y1 - y2__ x1 - x2 = __3 - 1__ -1 - 2 =2/-3

2. Find the slope of the altitude. The slope of the altitude is 3/2 because perpendicular lines are always negative recipricals.

3. Find equation of altitude using point C y=mx+b 1=3/2(2/1)+b 1=6/2+b 1=3+b 1-3=b -2=b the equation of the altitude is y=3x-2 How to find the equation of AC:

1. Find slope of AC M = __y1 - y2__ x1 - x2 = __3 - 1__ -1 - 2 =2/-3

2. Now sub in A y = mx+b 3 = 2/-3 (-1/1) + b 3 = -2/-3 + b 3/1(3) - 2/3 = b 9/3 - 2/3 = b 7/3 = b

the equation of AC equals y=2/-3 =7/3, you use substitution to find the POI for this question

Substitution:

1. y = 2/-3 + 7/3 2. y = 3x - 2

Substitute 1 into 2

7/3(3) - 2/3x(3) = 3x(3) - 2(3) 7 - 3x = 9x - 6 -3x - 9x = - 7 - 6 -12x= -13 -12x = -13 -12x/12 = 13/12

Subsitute x = 13/12 into 1

1. y= -2/3 (13/12) + 7/3

y = -26/-36 +7/3 y = 13/18 + 7/6(3) y = 13/18 +42/18 y = 55/18 POI is (13/12, 55/18)

Find the length between the POI and the point B(-2,-1)

L = (x1-x2)2 + (y1-y2)2 L = (13/2 + 2/1)2 + (55/18 + 1/1)2 L = (37/12)2 +(73/18)2 L = 0.257 + 0.225 L = 0.48