Applications of the Distance Formula Unit 4 Day 9

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

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

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 = 6−2 2 + 3−3 2 AB = 4 2 +0 AB = 16 AB = 4 C A B

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 = 2−2 2 + 7−3 2 AC = 0+ 4 2 AC = 16 AC = 4 C A B

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 = 2−6 2 + 7−3 2 BC = −4 2 + 4 2 BC = 16+16 BC = 32 BC = 4 2 ≈5.66 A B C

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

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− −3 2 + 11−5 2 CP = 8 2 + 6 2 CP = 64+36 CP = 100 CP = 10 Radius = 10

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 2 + −2−5 2 CP = 25+49 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