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Geometry/Perpendicular Bisector

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Question
Q: Hi! Thank you for your time. My question is "Which equation represents the perpendicular bisector of AB whose endpoints are A(8,2) and B(0,6)?

Answer choices: (1) y=2x-4 (2) y=-1/2x+2 (3) y=-1/2x+6 (4) y=2x-12

Answer
Hi Meagan,

The perpendicular bisector of AB has the slope that is the negative reciprocal of that of AB, and it passes through the midpoint of AB.

Find the slope of AB.
(2-6)/(8-0)=-1/2

Take the negative reciprocal.
-(-1/2)^(-1)=2

Find the midpoint of AB.
(8+0,2+6)/2=(4,4)

Select the choice that fits these conditions.


Thanks for asking,
Azeem

Geometry

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Azeem Hussain

Expertise

I welcome your questions on algebra, 2D and 3D geometry, parabolic functions and conic sections, and any other mathematical queries you may have.

Experience

4 years as a drop-in and by-appointment tutor at Champlain College. Private tutor for dozens of clients over the past 8 years.

Publications
CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry

Education/Credentials
Bachelor of Science, Major Mathematics and Major Economics, McGill University, 2014. Diploma of Collegiate Studies; Pure and Applied Science, Champlain College Saint-Lambert, 2010.

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