Perimeters, Midpoints, and Parallel lines

1. Find the perimeter and midpoints of any triangle.

2. Identify parallel lines.

Today’s goalsBy the end of class today, YOU should be able to…

The Distance Formula

d = √(x2-x1)2+(y2-y1)2

The distance, d, between any points with coordinates (x1, y1) and (x2, y2) can be found by using the distance formula.

Ex.1: Finding the distance between two points of a triangle

Find the distance between the pair of points with the given coordinates: (4,12) (4,10)

Ex.1: Solution

(4 , 12) (4 , 10)x1 y1 x2 y2

Label x & y values

d = √(12-4)2+(10-4)2Plug values into distance formula: d = √(x2-x1)2+(y2-y1)2

d = √(8)2+(6)2 Solve for values inside the parentheses

d = √64+36 = √100 Square 8 and 6, them add them together

d = 10 Take the square root of 100

You try…

Find the distance between the pair of points with the given coordinates:

(7,7) (-5,-2)

(-1,4) (1,4)

Review

What is perimeter?

The total distance around an object.

You try… finding the perimeter of atriangle

Find the perimeter of a triangle with the given coordinates: (3,-5) (3,4) (0, 2)

HINT: Use the distance formula

The Midpoint Formula

M = ((x1+x2)⁄2 , (y1+y2)⁄2)

The middle point of a line segment is called the midpoint. It is equidistant from both endpoints.

Ex.2: Finding the midpoint of a line segment

Find the midpoint of a line segment with the given coordinates: (7,8) (5,10)

Ex.2: Solution

(7 , 8) (5 , 10)x1 y1 x2 y2

Label x & y values

M = ((7+5)/2 , (8+10)/2)Plug values into midpoint formula: M = ((x1+x2)⁄2 , (y1+y2)⁄2)

M = (12/2 , 18/2) Solve for values inside the parentheses

M =(6,9) Solve for x and y by dividing each value by 2

You try…

Find the midpoints of the line segments with the given coordinates:

1. (3,4) (5,4)

2. (3,9) (-2,-3)

Review

Parallel lines are two lines in a plane that never intersect or meet. The parallel symbol is ll. For

example, AB ll CD indicates that line AB is parallel to line CD.