1. Applications of the Distance Formula
Unit 4 Day 9

2. Classifying Triangles by Sides
Scalene Triangle
Isosceles Triangle
Equilateral Triangle
No congruent sides
At least 2 congruent sides
3 congruent sides

3. Classifying Triangles by Angles
Acute Triangle
Right Triangle
Obtuse Triangle
Equiangular Triangle
3 acute angles
1 right angle
1 obtuse angle
3 congruent angles

4. Example 1
A triangle has the given vertices. Graph the triangle and classify it by its sides. Then determine if it is a right triangle.
A(2,3), B(6,3), C(2,7)
AB = 6− −3 2
AB =
AB = 16
AB = 4 C A B

5. Example 1 Continued
A triangle has the given vertices. Graph the triangle and classify it by its sides. Then determine if it is a right triangle.
A(2,3), B(6,3), C(2,7)
AC = 2− −3 2
AC =
AC = 16
AC = 4 C A B

6. Example 1 Continued
A triangle has the given vertices. Graph the triangle and classify it by its sides. Then determine if it is a right triangle.
A(2,3), B(6,3), C(2,7)
BC = 2− −3 2
BC = −
BC =
BC = 32
BC = 4 2 ≈5.66 A B C

7. Example 1 Continued
A triangle has the given vertices. Graph the triangle and classify it by its sides. Then determine if it is a right triangle.
A(2,3), B(6,3), C(2,7)
AB = 4
AC = 4
BC = 4 2 ≈5.66
2 congruent sides:
Isosceles Triangle
1 Right Angle:
Right Triangle A B C

8. Example 2
The center of a circle is C(-3, 5) and the point P(5,11) is on the circle. Find the radius of the circle.
CP = 5− − −5 2
CP =
CP =
CP = 100
CP = 10
Radius = 10

9. Example 3
A circle has its center at (-2,5) and a radius of 5. For the point below determine whether the point is on the circle, inside the circle, or outside the circle. Justify your answers.
(3, -2)
CP = 3− − −2−5 2
CP =
CP = 74 ≈8.60
(3,-2) lies outside the circle because 8.60 >5
If the distance between the Center and the Point (CP) :
CP > r
P is outside
CP = r
P is on
CP < r
P is inside