Chapter 5 unit f 002 12
- 1. 2.21 Drill 12/21/12 Use the diagram for Items 1–2. 1. Given that m ABD = 16°, find m ABC. 32° 2. Given that m ABD = (2x + 12)° and m CBD = (6x – 18)°, find m ABC. 54° Use the diagram for Items 3–4. 3. Given that FH is the perpendicular bisector of EG, EF = 4y – 3, and FG = 6y – 37, find FG. 65 4. Given that EF = 10.6, EH = 4.3, and FG = 10.6, find EG. 8.6
- 2. A locus is a set of points that satisfies a given condition. The perpendicular bisector of a segment can be defined as the locus of points in a plane that are equidistant from the endpoints of the segment.
- 3. Example 4: Writing Equations of Bisectors in the Coordinate Plane Write an equation in point-slope form for the perpendicular bisector of the segment with endpoints C(6, –5) and D(10, 1). Step 1 Graph . The perpendicular bisector of is perpendicular to at its midpoint.
- 4. Example 4 Continued Step 2 Find the midpoint of . Midpoint formula. mdpt. of =
- 5. Example 4 Continued Step 3 Find the slope of the perpendicular bisector. Slope formula. Since the slopes of perpendicular lines are opposite reciprocals, the slope of the perpendicular bisector is
- 6. Example 4 Continued Step 4 Use point-slope form to write an equation. The perpendicular bisector of has slope and passes through (8, –2). y – y1 = m(x – x1) Point-slope form Substitute –2 for y1, for m, and 8 for x1.