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Understanding Midpoints and Distances on the Coordinate Plane

Explore the concept of midpoints and distances in the coordinate plane. Recall the Pythagorean Theorem and its application in finding distances between points. Practice finding midpoints and distances using formulas and ordered pairs. Solve problems to enhance your understanding of coordinate geometry.

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Understanding Midpoints and Distances on 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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