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

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Presentation transcript:

Distance & Midpoint Formulas Sections covered: 1.8 The Coordinate Plane

Review: Coordinate Plane

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

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

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

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

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

Simplifying Radicals

Distance Formula

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

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?