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Warm Up 1. Graph A (–2, 3) and B (1, 0).

Warm Up 1. Graph A (–2, 3) and B (1, 0). 2. Find CD. 8. 3. What is Perimeter?. In a plane figure, the perimeter is the sum of the distances of each side.

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Warm Up 1. Graph A (–2, 3) and B (1, 0).

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  1. Warm Up • 1. Graph A (–2, 3) and B (1, 0). 2. Find CD. 8 3. What is Perimeter? In a plane figure, the perimeter is the sum of the distances of each side.

  2. 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).

  3. The midpoint of a segment is the AVERAGE of the two endpoints!

  4. Example 1: Finding the Coordinates of a Midpoint Find the coordinates of the midpoint of PQ with endpoints P(–8, 3) and Q(–2, 7). = (–5, 5)

  5. Try your own: Example 1 Find the coordinates of the midpoint of EF with endpoints E(–2, 3) and F(5, –3).

  6. Step 2 Use the Midpoint Formula: 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).

  7. – 2 – 7 –2 –7 Example 2 Continued Step 3 Find the x-coordinate. Set the coordinates equal. Multiply both sides by 2. 12 = 2 + x Simplify. 2 = 7 + y Subtract. –5 = y 10 = x Simplify. The coordinates of Y are (10, –5).

  8. S is the midpoint of RT. R has coordinates (–6, –1), and S has coordinates (–1, 1). Find the coordinates of T. Step 2 Use the Midpoint Formula: Try your own: Example 2 Step 1 Let the coordinates of T equal (x, y).

  9. + 1 + 1 + 6 +6 Example 2 Continued Step 3 Find the x-coordinate. Set the coordinates equal. Multiply both sides by 2. –2 = –6 + x Simplify. 2 = –1 + y Add. 4 = x Simplify. 3 = y The coordinates of T are (4, 3).

  10. Find FG and JK. Then determine whether FG ≅JK. Example 3: Using the Distance Formula Step 1 Find the coordinates of each point. F(1, 2), G(5, 5) J(–4, 0), K(–1, –3)

  11. Example 3 Continued Step 2 Use the Distance Formula.

  12. 1. Find the coordinates of the midpoint of MN with endpoints M(-2, 6) and N(8, 0). 2.K is the midpoint of HL. H has coordinates (1, –7), and K has coordinates (9, 3). Find the coordinates of L. Lesson Quiz: Part I (3, 3) (17, 13) 3. Find the distance, to the nearest tenth, between S(6, 5) and T(–3, –4). 12.7 4. The coordinates of the vertices of ∆ABC are A(2, 5), B(6, –1), and C(–4, –2). Find the perimeter of ∆ABC, to the nearest tenth. 26.5

  13. 5. Find the lengths of AB and CD and determine whether they are congruent. Lesson Quiz: Part II

  14. 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).

  15. Example 4 Continued Method 1 Use the Distance Formula. Substitute the values for the coordinates of D and E into the Distance Formula.

  16. Example 4 Continued Method 2 Use the Pythagorean Theorem. Count the units for sides a and b. a = 5 and b = 9. c2 =a2 + b2 =52 + 92 =25 + 81 =106 c =10.3

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