Perpendicular Bisector Worksheet
Grade 11 Geometry worksheet focusing on understanding, constructing, and applying perpendicular bisectors in various geometric contexts.
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Perpendicular Bisector Worksheet
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Read each question carefully and answer to the best of your ability. Show all your work for full credit.
1. Define a perpendicular bisector in your own words. What two key properties must a line possess to be considered a perpendicular bisector of a segment?
2. Any point on the perpendicular bisector of a segment is from the endpoints of the segment. This is known as the Theorem.
3. The intersection of the perpendicular bisectors of the sides of a triangle is called the . This point is equidistant from the of the triangle.
4. Given a segment with endpoints A(2, 5) and B(8, 1).
a) Find the midpoint of segment AB.
b) Find the slope of segment AB.
c) Determine the slope of the perpendicular bisector of segment AB.
d) Write the equation of the perpendicular bisector of segment AB in slope-intercept form (y = mx + b).
5. Plot the points A(2, 5) and B(8, 1) and the perpendicular bisector you found in question 4 on the coordinate plane below.
6. Which of the following is true about the perpendicular bisector of a segment?
It is parallel to the segment.
It intersects the segment at one of its endpoints.
It forms a 90-degree angle with the segment and passes through its midpoint.
It is always shorter than the segment it bisects.
7. Imagine three towns, A, B, and C, are located such that they form a triangle. A new hospital needs to be built an equal distance from towns A and B. Describe the geometric locus of all possible locations for the hospital.
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