1 / 5

Find the center of the circle that circumscribes XYZ .

Find the center of the circle that circumscribes XYZ . Because X has coordinates (1, 1) and Y has coordinates (1, 7), XY lies on the vertical line x = 1. The perpendicular bisector of XY is the horizontal line that passes through (1, ) or (1, 4), so the equation

yanisin
Download Presentation

Find the center of the circle that circumscribes XYZ .

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. Find the center of the circle that circumscribes XYZ. Because X has coordinates (1, 1) and Y has coordinates (1, 7), XY lies on the vertical line x = 1. The perpendicular bisector of XY is the horizontal line that passes through (1, ) or (1, 4), so the equation of the perpendicular bisector of XY is y = 4. 1 + 7 2 Because X has coordinates (1, 1) and Z has coordinates (5, 1), XZ lies on the horizontal line y = 1. The perpendicular bisector of XZ is the vertical line that passes through ( , 1) or (3, 1), so the equation of the perpendicular bisector of XZ is x = 3. 1 + 5 2 Concurrent Lines, Medians, and Altitudes LESSON 5-3 Additional Examples

  2. The lines y = 4 and x = 3 intersect at the point (3, 4). This point is the center of the circle that circumscribes XYZ. Concurrent Lines, Medians, and Altitudes LESSON 5-3 Additional Examples (continued) Quick Check

  3. The roads form a triangle around the park. Concurrent Lines, Medians, and Altitudes LESSON 5-3 Additional Examples City planners want to locate a fountain equidistant from three straight roads that enclose a park. Explain how they can find the location. Theorem 5-7 states that the bisectors of the angles of a triangle are concurrent at a point equidistant from the sides. The city planners should find the point of concurrency of the angle bisectors of the triangle formed by the three roads and locate the fountain there. Quick Check

  4. M is the centroid of WOR, and WM = 16. Find WX. 2 3 Because M is the centroid of WOR, WM = WX. 2 3 WM = WXTheorem 5-8 2 3 16 = WXSubstitute 16 for WM. 3 2 24 = WXMultiply each side by . Concurrent Lines, Medians, and Altitudes LESSON 5-3 Additional Examples The centroid is the point of concurrency of the medians of a triangle. The medians of a triangle are concurrent at a point that is two thirds the distance from each vertex to the midpoint of the opposite side. (Theorem 5-8) Quick Check

  5. Is KX a median, an altitude, neither, or both? Because LX = XM, point X is the midpoint of LM, and KX is a median of KLM. Because KX is perpendicular to LM at point X, KX is an altitude. So KX is both a median and an altitude. Concurrent Lines, Medians, and Altitudes LESSON 5-3 Additional Examples Quick Check

More Related