Distance & Midpoint Formulas Sections covered: 1.8 The Coordinate Plane.

Distance & Midpoint FormulasSections covered:1.8 The Coordinate Plane

Review: Coordinate Plane

Algebra Review• Evaluate the expression for m = -3 and n = 7.

2nm

Algebra Review• Evaluate the expression for m = -3 and n = 7.

2mn

Algebra Review• Evaluate the expression for m = -3 and n = 7.

22 nm

Algebra Review• Evaluate the expression for a = 6 and b = -8.

22 ba

Algebra Review• Evaluate the expression for a = 6 and b = -8.

2

ba

Simplifying Radicals

16

Simplifying Radicals

8

Simplifying Radicals

324

Simplifying Radicals

500

Distance Formula

2122

12 yyxxd

Example 1• Find the distance between T(5,2) and R(-4,-1) to the nearest tenth.

Example 2• Find the distance between A(-1,5) and B(0,4). Leave in simplest

radical form.

Example 3• Each morning Juanita takes the Blue Line subway from

Oak Station to Jackson Station. Oak Station is 1 mile west and 2 miles south of City Plaza. Jackson Station is 2 miles east and 4 miles north of City Plaza. Find the distance Juanita travels between the two stations.

The Midpoint Formula

2

,2

2121 yyxxM

Example 4• QS has endpoints Q(3,5) and S(7,-9). Find the coordinates of its

midpoint M.

Example 5• Find the midpoint of segment EF, with E(-7,0) and F(5,8).

Example 6• The midpoint of AB is M(3,4). One endpoint is A(-3,-2). Find the

coordinates of the other endpoint B.

Example 7• GH has endpoints G(-3,2) and H(3,-2). Find the coordinates of its

midpoint.

End of Notes

•Please pick up a whiteboard, a marker, and an eraser.

Example 8

• On your whiteboard, graph the following points:• A(2,1), B(6,-1), C(8,7), D(4,9)• Draw quadrilateral ABCD.• Use the Midpoint Formula to find the midpoints of each side.• What appears to be true?

Example 9• A boat at the point X(5,-2) needs to travel to Y(-6,9) or Z(17,-

3). Which point is closer?

• What is the distance to the closer point?