CN#6 Objectives. Vocabulary 9/21/18. coordinate plane leg hypotenuse

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1 CN#6 Objectives G-GPE 7 7. Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula. coordinate plane leg hypotenuse Vocabulary Develop and apply the formula for midpoint. Use the Distance Formula and the Pythagorean Theorem to find the distance between two points. 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. Helpful Hint To make it easier to picture the problem, plot the segment s endpoints on a coordinate plane. 1

X has coordinates (2, 7) and M has coordinates (6, 1). Find the coordinates of Y. Step 1 Let the coordinates of Y equal (x, y).

2 Example 1: Finding the Coordinates of a Midpoint Check It Out! Example 1 Find the coordinates of the midpoint of PQ with endpoints P( 8, 3) and Q( 2, 7). Find the coordinates of the midpoint of EF with endpoints E( 2, 3) and F(5, 3). = ( 5, 5) Example 2: Finding the Coordinates of an Endpoint M is the midpoint of XY. X has 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 2 Use the Midpoint Formula: Example 2 Continued Step 3 Find the x-coordinate. Set the coordinates equal. Multiply both sides by = 2 + x Simplify. 2 2 Subtract. 10 = x Simplify. 2 = 7 + y = y The coordinates of Y are (10, 5). 2

Check It Out! Example 2 S is the midpoint of RT. R has coordinates ( 6, 1), and S has coordinates ( 1, 1). Find the coordinates of T. Step 1 Let the coordinates of T equal (x, y).

3 Check It Out! Example 2 S is the midpoint of RT. R has coordinates ( 6, 1), and S has coordinates ( 1, 1). Find the coordinates of T. Step 1 Let the coordinates of T equal (x, y). Step 2 Use the Midpoint Formula: Check It Out! Example 2 Continued Step 3 Find the x-coordinate. Set the coordinates equal. Multiply both sides by 2. 2 = 6 + x Simplify Add. 2 = 1 + y = x Simplify. 3 = y The coordinates of T are (4, 3). Example 3: Using the Distance Formula The Ruler Postulate can be used to find the distance between two points on a number line. The Distance Formula is used to calculate the distance between two points in a coordinate plane. Find FG and JK. Then determine whether JK. Step 1 Find the coordinates of each point. F(1, 2), G(5, 5), J( 4, 0), K( 1, 3) 3

Example 3 Continued Step 2 Use the Distance Formula. Check It Out! Example 3 Find EF and GH. Then determine if EF @ GH. Step 1 Find the coordinates of each point.

4 Example 3 Continued Step 2 Use the Distance Formula. Check It Out! Example 3 Find EF and GH. Then determine if GH. Step 1 Find the coordinates of each point. E( 2, 1), F( 5, 5), G( 1, 2), H(3, 1) Check It Out! Example 3 Continued Step 2 Use the Distance Formula. You can also use the Pythagorean Theorem to find the distance between two points in a coordinate plane. You will learn more about the Pythagorean Theorem in Chapter 5. 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. 4

5 Example 4: Finding Distances in the Coordinate Plane Use the Distance Formula and the Pythagorean Theorem to find the distance, to the nearest tenth, from D(3, 4) to E( 2, 5). 5

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Lesson. Skills Practice Name Date Let s Get This Started! Points, Lines, Planes, Rays, and Line Segments Vocabulary Write the term that best completes each statement.. A geometric figure created without