1. 2.7 Coordinate Proofs

2. (Definitely not all the options!)
Coordinate proofs use coordinates on a graph
1) specific points (using numbers)
Going to have to pull from your Geometry days!
Things to Remember:
- For a quadratic ax2 + bx + c = y
if a > 0  right side up
if a < 0  upside down
- Perimeter of rectangle:
- Distance Formula:
- Midpoint Formula:
- Parallel lines have same slope
- Isosceles triangles have 2 sides = length
- Equilateral triangles have all 3 sides = length
- Collinear points:
- DRAW A PICTURE!!!
2) general points (using letters)
shapes, distances, slopes, midpoints, etc.
 vertex is a minimum
 vertex is a maximum
2l + 2w
(Definitely not all the options!)
Let’s try some!
AB + BC = AC

3. w = where it hits parabola = the y-value = y = 7 – 3x2
Ex 1) Determine the maximum perimeter of a rectangle inscribed in a parabolic arch modeled by y = 7 – 3x2 so the base of the rectangle is along the x-axis.
P = 2l + 2w 7
l = 2(x-value) = 2x
w = where it hits parabola
= the y-value
= y = 7 – 3x2 x
P = 2(2x) + 2(7 – 3x2)
= 4x + 14 – 6x2
P = – 6x2 + 4x + 14
want max perimeter, so the vertex

4. Ex 2) Are the points collinear
Ex 2) Are the points collinear? A(2, 6) B(–4, 3) C(0, 5) (If yes, 2 lengths should add up to 3rd one)
largest
Does
 yes!
so the points are collinear

5. Ex 3) Determine whether the points A(–1, –3), B(–5, 2), & C(3, 4) form an acute or obtuse triangle.
Use a “version of Pythagorean Theorem”
(largest)2 < or > (other)2 + (other)2
< means acute △
<

6. Ex 4) Prove that the length of the line segment joining the midpoints of 2 sides of a triangle is half the length of the third side.
B (2b, 2c) M N A C
(0, 0)
(2a, 0)

7. Homework
#208 Pg #1, 2, 4, 6, 8, 10, 18, 19, 23