Distance, Midpoint, Pythagorean Theorem

Distance Formula• Distance formula—used to measure the

distance between between two endpoints of a line segment (on a graph).

d x x y y ( ) ( )1 22

1 22

• x1 and y1 are the coordinates of the first point

• x2 and y2 are the coordinates of the second point

Distance Formula

• Find the distance between the points (1, 2) and (–2, –2).

• Your video game uses a coordinate grid system for location. There is an enemy ship at (7, –3). You are at (–8, –3). If one grid unit equals 10 miles, how far away is the enemy ship?

Midpoint Formula• Midpoint formula—used to find the

midpoint of a line segment. (It will always be in the form of a point (x, y).)

2

,2

2121 yyxxM

• x1 and x2 are the x-coordinates of the points

• y1 and y2 are the y-coordinates of the points

Midpoint Formula

• Find the midpoint of the segment given the endpoints (5, 7) and (13, 1).

• What is the midpoint of the line segment with endpoints (–3, –3) and (7, 3)?

• Line segment CD has a midpoint at (1, 2). If endpoint C is located at (–5, 3), find the ordered pair represented the other endpoint D.

Pythagorean Theorem

• Pythagorean Theorem—In a right triangle, the sum of the squares of the two legs equals the hypotenuse squared.

• a2 + b2 = c2

a and b are legs

c is the hypotenuse

Pythagorean Theorem

leg

leg

hypotenuse

The hypotenuse is always the longest side of a right triangle and is always opposite the right angle.

Pythagorean Theorem

• What is the value of the missing side?

5

12

Pythagorean Theorem

• What is the value of the missing side?

9 15

Pythagorean Theorem

• The perimeter of a square is 36 inches. What is the length of its diagonal?

Homework• Pg. 552 (#10, 11, 14, 15, 22-27)

• Pg. 557 (#10-18 find distance AND midpoint)