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Chapter 1 Section 6 Midpoint and Distance in the Coordinate Plane

Chapter 1 Section 6 Midpoint and Distance in the Coordinate Plane. Warm Up – Journal Entry Today’s date: In 2 – 3 sentences, write what you remember about the Pythagorean Theorem from previous classes.

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Chapter 1 Section 6 Midpoint and Distance in the Coordinate Plane

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  1. Chapter 1 Section 6 Midpoint and Distance in the Coordinate Plane

  2. Warm Up – Journal Entry Today’s date: In 2 – 3 sentences, write what you remember about the Pythagorean Theorem from previous classes.

  3. A coordinate planeis a plane that is divided into four regions by a horizontal line (x-axis) and a vertical line (y-axis) . The location, or coordinates, of a point are given by an ordered pair (x, y). y x

  4. point 1 point 2

  5. In a right triangle, the two sides that form the right angle are the legs. The side across from the right angle is the hypotenuse. In the diagram, a and b are legs of the right triangle. The longest side is called the hypotenuse and has length c. a

  6. Problem 1 Find the coordinates of the midpoint of EF with endpoints E(–2, 3) and F(5, –3).

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

  8. Step 2 Use the Midpoint Formula: Problem 3 M is the midpoint of XY. Xhas coordinates (2, 7) and M has coordinates (6, 1). Find the coordinates of Y. Step 1 Let the coordinates of Y equal (x, y). Step 3 Find the x-coordinate. Step 4 Find the y-coordinate. y x The coordinates of Y are (10, –5).

  9. S is the midpoint of RT. Rhas coordinates (–6, –1), and S has coordinates (–1, 1). Find the coordinates of T. Step 2 Use the Midpoint Formula: Problem 4 Step 1 Let the coordinates of T equal (x, y). y Step 4 Find the y-coordinate. Step 3 Find the x-coordinate. x The coordinates of T are ( , ).

  10. Find FG and JK. Then determine whether FG  JK. Problem 5 F(2 , 1), G( 5, 5), J(-4,0), K( -1,-3)

  11. Find EF and GH. Then determine if EF  GH. Problem 6 E(–2, 1), F(–5, 5), G(–1, –2), H(3, 1) Step 1 Find the coordinates of each point. Step 2 Use the Distance Formula.

  12. Problem 7 Use the Distance Formula and the Pythagorean Theorem to find the distance, to the nearest tenth, from D(3, 4) to E(–2, –5).

  13. Problem 8 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)

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