Question

three friends want to meet at a place that is the same distance from each of their houses. they draw a map and measure the approximate distances and angles, as shown. jo’s house 38° 0.5 miles 0.6 miles 88° boris’s house 0.4 miles 54° carrie’s house which step should they take next to find a meeting place that is the same distance from each person’s house? find the midpoint of the segments which connect their houses. bisect each of the angles with vertices at their houses. draw perpendicular lines through any point on the segments which connect their houses. draw perpendicular line segments from each vertex to the opposite side.

Explanation:

To find a point equidistant from three vertices of a triangle (the friends' houses), we use the concept of the circumcenter. The circumcenter is the intersection of the perpendicular bisectors of the triangle's sides. The midpoint of a side is part of finding the perpendicular bisector. Bisecting angles finds the incenter (equidistant from sides, not vertices). Drawing perpendiculars through any point or from vertices to opposite sides (altitudes) don't relate to equidistance from vertices. So finding midpoints of the segments (sides) is the first step toward drawing perpendicular bisectors.

Answer:

Find the midpoint of the segments which connect their houses.