Lesson 86 Warm Up Pg. 563

Algebra 1 Lesson 86 Calculating the Midpoint and Length of a Segment

Example 1 The diagram shows a grid of city streets. A car travels from point P to point Q by moving east to point R and then south to point Q. What is the direct distance (in city blocks) from point P to point Q? PR Q 5th 4th 3rd 2nd 1st Avenues A B C D E GF Streets

The Distance Formula The distance d between two points (x 1, y 1 ) and (x 2, y 2 ) is d = √ (x 2 -x 1 ) 2 + (y 2 -y 1 ) 2.

Example 2 Find the distance between (3, -2) and (6, 4).

Example 3 In quadrilateral ABCD, point A is (-1,0), point B is (2,1), point C is (1, -2), and point D is at (-2, -3). Determine whether the quadrilateral is a rhombus.

Midpoint The midpoint of a line segment is the point that divides the segment into two equal-length segments. The midpoint M of the line segment with endpoints (x 1, y 1 ) and (x 2, y 2 ) is M=(x 1 +x 2, y 1 +y 2 ). 2 2

Example 4 Find the midpoint of the line segment with the given endpoints. (3, 5) and (7, -2)

Example 5 A coordinate plane can be used to model positions of players on a football field. A quarterback is on the 30-yard line at (30, 10). He throws a pass to his receiver who is on the 50 yard line at (50, 40). Find the length of the pass as a radical in simplest form. Then use a calculator to estimate the length to the nearest yard.

Lesson 86 Homework Pg. 566 Practice, WS #86