MYTUTOR SUBJECT ANSWERS

557 views

What is the perpendicular bisector of the point (0,2) and (1,0)?

First things first it will definately be useful to make a quick sketch of the x-y axes, the two points, and roughtly what the perpendicular bisector will look like.

This kind of question can be made much more painless if you make the following observation: for any point (x,y) on the perpendicular bisector (lets call this P) the distance from (x,y) to (0,2) and the distance from (x,y) to (1,0) are equal. 

Let (x,y) lie on P. Using Pythagoras' Theorem the distance (x,y) to (0,2) is  sqrt[(x - 0)2 +  (y - 2)2]. Similairly the distance from (x,y) to (1,0) is sqrt[(x - 1)2 + (y - 0)2]. These two distances must then be equal so:

 sqrt[(x - 0)2 +  (y - 2)2] = sqrt[(x - 1)2 + (y - 0)2] , now squaring gives:

(x - 0)2 +  (y - 2)2 = (x - 1)2 + (y - 0)2 , then simplifying gives:

x2 + (y - 2)2 = (x - 1)2 + y2 , expanding the brackets gives:

x2 + y2 - 4y +4 = x- 2x +1 + y2 , then cancelling the x2 and y2 terms:

-4y + 4 = -2x + 1 , which rearranges to give the line:

y = x/2 + 3/4 

There was nothing special here about finding the perpendicular bisector of (0,2) and (1,0), the exact some method can be used for any two points in the plane. The only thing that must be altered is our two expressions for the distances from (x,y) to the first point and the distance form (x,y) to the second. 

Josh R. GCSE Maths tutor, A Level Maths tutor, 13 plus  Maths tutor, ...

2 years ago

Answered by Josh, a GCSE Maths tutor with MyTutor


Still stuck? Get one-to-one help from a personally interviewed subject specialist

456 SUBJECT SPECIALISTS

£18 /hr

Sara D.

Degree: Computer Science and Mathematics (Bachelors) - Edinburgh University

Subjects offered: Maths, Computing

Maths
Computing

“Top tutor from the renowned Russell university group, ready to help you improve your grades.”

£30 /hr

James B.

Degree: Management (Bachelors) - Bristol University

Subjects offered: Maths, Physics+ 2 more

Maths
Physics
ICT
Chemistry

“Hi there! I am currently a 2nd year Management student at the University of Bristol. I originally took Computer Science but switched to Management after 2 years of study. During my school life I was always very Science-based, studying...”

£18 /hr

Upasana T.

Degree: Medicine (Bachelors) - Birmingham University

Subjects offered: Maths, Latin+ 1 more

Maths
Latin
Biology

“About me: Hi, my name is Upasana Topiwala and I am currently in my third year of medical school at the university of Birmingham. I've taken up tutoring in order to inspire my students to appreciate the importance of science in our liv...”

About the author

£24 /hr

Josh R.

Degree: Mathematics (Masters) - Warwick University

Subjects offered: Maths, Further Mathematics

Maths
Further Mathematics

“I study Maths at Warwick, I hope to be able to teach your child to love Maths and how to achieve top exam grades. ”

You may also like...

Other GCSE Maths questions

The circle c has equation x^2 + y^2 = 1. The line l has gradient 3 and intercepts the y axis at the point (0, 1). c and l intersect at two points. Find the co-ordinates of these points.

How do you work out the old price of an item having been given the new price after a specified percentage change?

Find the equation of the line passing through the point ( 2, −3) which is parallel to the line with equation y + 4x = 7

Prove that (2n+3)^2-(2n-3)^2 is a multiple of 8 for positive integer values of n

View GCSE Maths tutors

Cookies:

We use cookies to improve our service. By continuing to use this website, we'll assume that you're OK with this. Dismiss

mtw:mercury1:status:ok