1 / 13

Example 7-1a

Let A , B , C , and D be vertices of a rectangle with sides a units long, and sides b units long. Place the square with vertex A at the origin, along the positive x -axis, and along the y -axis. Label the vertices A , B , C , and D. Example 7-1a.

wynn
Download Presentation

Example 7-1a

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Let A, B, C, and D be vertices of a rectangle with sides a units long, and sides b units long. Place the square with vertex A at the origin, along the positive x-axis, and along the y-axis. Label the vertices A, B, C, and D. Example 7-1a Position and label a rectangle with sides a and bunits long on the coordinate plane. The y-coordinate of B is 0 because the vertex is on the x-axis. Since the side length is a, the x-coordinate is a.

  2. The x-coordinate of C is also a. The y-coordinate is b because the side is b units long. Example 7-1b D is on the y-axis so the x-coordinate is 0. Since the side length is b, the y-coordinate is b. Sample answer:

  3. Example 7-1c Position and label a parallelogram with sides a and bunits long on the coordinate plane. Sample answer:

  4. The legs of an isosceles trapezoid are congruent and have opposite slopes. Point C is c units up and b units to the left of B. So, point D is c units up and b units to the right of A. Therefore, the x-coordinate of D is and the y-coordinate of D is Answer: Example 7-2a Name the missing coordinates for the isosceles trapezoid.

  5. Answer: Example 7-2b Name the missing coordinates for the rhombus.

  6. Example 7-3a Place a rhombus on the coordinate plane. Label the midpoints of the sides M, N, P, and Q. Write a coordinate proof to prove that MNPQ is a rectangle. The first step is to position a rhombus on the coordinate plane so that the origin is the midpoint of the diagonals and the diagonals are on the axes, as shown. Label the vertices to make computations as simple as possible. Given:ABCD is a rhombus as labeled. M, N, P, Q are midpoints. Prove: MNPQ is a rectangle.

  7. Find the slopes of Example 7-3b Proof: By the Midpoint Formula, the coordinates of M, N, P, and Qare as follows.

  8. slope of slope of slope of slope of Example 7-3c

  9. Example 7-3c A segment with slope 0 is perpendicular to a segment with undefined slope. Therefore, consecutive sides of this quadrilateral are perpendicular. Since consecutive sides are perpendicular, MNPQ is, by definition, a rectangle.

  10. Example 7-3d Place an isosceles trapezoid on the coordinate plane. Label the midpoints of the sides M, N, P, and Q. Write a coordinate proof to prove that MNPQ is a rhombus. Given:ABCD is an isosceles trapezoid. M, N, P, and Q are midpoints. Prove:MNPQ is a rhombus.

  11. Proof: The coordinates of M are (–3a, b); the coordinates of N are(0, 0); the coordinates of P are (3a, b); the coordinates of Q are (0, 2b). Since opposite sides haveequal slopes, opposite sides are parallel. Since all four sides are congruent and opposite sides are parallel, MNPQ is a rhombus. Example 7-3e

  12. Prove: Since have the same slope, they are parallel. Example 7-4a Write a coordinate proof to prove that the supports of a platform lift are parallel. Given:A(5, 0), B(10, 5), C(5, 10), D(0, 5) Proof:

  13. Prove: Proof: Since have the same slope, they are parallel. Example 7-4b Write a coordinate proof to prove that the crossbars of a child safety gate are parallel. Given:A(–3, 4), B(1, –4), C(–1, 4), D(3, –4)

More Related