1 / 6

EXAMPLE 4

Place an isosceles right triangle in a coordinate plane. Then find the length of the hypotenuse and the coordinates of its midpoint M. SOLUTION.

leone
Download Presentation

EXAMPLE 4

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. Place an isosceles right triangle in a coordinate plane. Then find the length of the hypotenuse and the coordinates of its midpoint M. SOLUTION Place PQOwith the right angle at the origin. Let the length of the legs be k. Then the vertices are located at P(0, k), Q(k, 0), and O(0, 0). EXAMPLE 4 Apply variable coordinates

  2. = = = = k 2 k k 2 2 = 0 + k , k +0 M( ) M( , ) 2 2 2 2 2 2 2 2 2 k + (– k) 2k k + k (k–0) + (0–k) EXAMPLE 4 Apply variable coordinates Use the Distance Formula to find PQ. PQ = Use the Midpoint Formula to find the midpoint Mof the hypotenuse.

  3. Write a coordinate proof of the Midsegment Theorem for one midsegment. E(q+p, r) D(q, r) = = GIVEN : PROVE : SOLUTION 1 DE is a midsegment of OBC. 2 DE OCand DE = OC STEP1 Place OBCand assign coordinates. Because you are finding midpoints, use 2p, 2q, and 2r. Then find the coordinates of Dand E. 2q + 2p, 2r + 0 2q + 0, 2r + 0 E( ) D( ) 2 2 2 2 EXAMPLE 5 Prove the Midsegment Theorem

  4. STEP 2 Prove DE OC. The y-coordinates of Dand Eare the same, so DEhas a slope of 0. OCis on the x-axis, so its slope is 0. 1 Because their slopes are the same, DE OC. 2 Prove DE = OC. Use the Ruler Postulate to find DEand OC. STEP3 = 2p 2p – 0 (q +p) – q OC= = p DE= So, the length of DEis half the length of OC EXAMPLE 5 Prove the Midsegment Theorem

  5. In Example 5, find the coordinates of F, the midpoint of OC. Then show that EF OB. ANSWER r 0 (p, 0); slope of EF = = , slope of OB = = , the slopes of EF and OB are both , making EF || OB. (q + p)  p 2r 0 2q 0 r r r q q q for Examples 4 and 5 GUIDED PRACTICE 7.

  6. Graph the points O(0, 0), H(m, n), and J(m, 0). Is OHJa right triangle? Find the side lengths and the coordinates of the midpoint of each side. ANSWER Sample: yes; OJ = m, JH = n, HO = m2 + n2, OJ: ( , 0), JH: (m, ), HO: ( , ) m n m n 2 2 2 2 for Examples 4 and 5 GUIDED PRACTICE 8.

More Related