1-6 midpoint and distance in the coordinate plane

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CHAPTER 1 1-6 Midpoint and distance in the coordinate plane

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Page 1: 1-6 Midpoint and distance in the coordinate plane

CHAPTER 11-6 Midpoint and distance in the

coordinate plane

Page 2: 1-6 Midpoint and distance in the coordinate plane

OBJECTIVES Students will be able to : Develop and apply the formula for

midpoint.

Use the Distance Formula and the Pythagorean Theorem to find the distance between two points.

Page 3: 1-6 Midpoint and distance in the coordinate plane

MIDPOINT FORMULA What is the midpoint ? Answer: It is the middle section of a line.

Is what divides a line in 2 congruent sections.

How can you find the midpoint of a line? You can find the midpoint of a segment by

using the coordinates of its endpoints. Calculate the average of the x-coordinates

and the average of the y-coordinates of the endpoints.

Page 4: 1-6 Midpoint and distance in the coordinate plane

MIDPOINT FORMULA

Page 5: 1-6 Midpoint and distance in the coordinate plane

EXAMPLE 1 Find the coordinates of the

midpoint of PQ with endpoints P(–8, 3) and Q(–2, 7).

Solution: midpoint formula

Page 6: 1-6 Midpoint and distance in the coordinate plane

EXAMPLE 2 Find the coordinates of the

midpoint of EF with endpoints E(–2, 3) and F(5, –3).

Solution: midpoint formula

Page 7: 1-6 Midpoint and distance in the coordinate plane

STUDENT GUIDE Do problems 2 and3 from page 47 from

book

Page 8: 1-6 Midpoint and distance in the coordinate plane

EXAMPLE 3 Lets do problems 1 and 2 from

worksheet

Page 9: 1-6 Midpoint and distance in the coordinate plane

STUDENT GUIDE Lets do problems 3 to 5 from worksheet

Page 10: 1-6 Midpoint and distance in the coordinate plane

EXAMPLE 4 M is the midpoint of XY. X has

coordinates (2, 7) and M has coordinates (6, 1). Find the coordinates of Y.

Solution:

Page 11: 1-6 Midpoint and distance in the coordinate plane

STUDENT GUIDED PRACTICE Lets do problems 4 to 5 from book page

47 Worksheet problems 21-23

Page 12: 1-6 Midpoint and distance in the coordinate plane

DISTANCE FORMULA What is the distance formula? . The Distance Formula is used to

calculate the distance between two points in a coordinate plane.

Page 13: 1-6 Midpoint and distance in the coordinate plane

EXAMPLE 5 Lets do distance formula worksheet

Page 14: 1-6 Midpoint and distance in the coordinate plane

PYTHAGOREAN THEOREM What is the Pythagorean theorem? Answer: Is the theorem we used in right

triangles to figure out a side of the triangle. You can also used it to find the distance

between two points in the coordinate plane. In a right triangle, the two sides that form

the right angle are the legs. The side across from the right angle that stretches from one leg to the other is the hypotenuse. In the diagram, a and b are the lengths of the shorter sides, or legs, of the right triangle. The longest side is called the hypotenuse and has length c.

Page 15: 1-6 Midpoint and distance in the coordinate plane

EXAMPLE 6 Use the Distance Formula and

the Pythagorean Theorem to find the distance, to the nearest tenth, from R to S.

R(3, 2) and S(–3, –1)

Page 16: 1-6 Midpoint and distance in the coordinate plane

EXAMPLE 6 CONTINUE Method 1 Use the Distance Formula. Substitute

the values for the coordinates of R and S into the Distance Formula.

Page 17: 1-6 Midpoint and distance in the coordinate plane

EXAMPLE 6 CONTINUE Method 2 Use the Pythagorean Theorem. Count

the units for sides a and b.

Page 18: 1-6 Midpoint and distance in the coordinate plane

EXAMPLE 7 DO problems 1-2 in worksheet

Page 19: 1-6 Midpoint and distance in the coordinate plane

STUDENT GUIDED PRACTICE Let students do Pythagorean

workshweet

Page 20: 1-6 Midpoint and distance in the coordinate plane

PYTHAGOREAN A player throws the ball from

first base to a point located between third base and home plate and 10 feet from third base.

What is the distance of the throw, to the nearest tenth?

Page 21: 1-6 Midpoint and distance in the coordinate plane

HOMEWORK DO problems 8-15 in the book page 47

Page 22: 1-6 Midpoint and distance in the coordinate plane

CLOSURE Today we saw the midpoint formula, the

distance formula and the Pythagorean Theorem.