MYTUTOR SUBJECT ANSWERS

906 views

Two points have coordinates (1,-6) and (-2,3). Find the equation of the line which joins them, and their midpoint.

To find the line's equation, you need the gradient and the y-intercept. The gradient is found using:

(y2-y1)/(x2-x1)

Or simply (change in y direction)/(change in x direction)

In this case, the gradient =(3+6)/(-2-1)=9/-3=-3

and so the equation of the line is in the form 

y=-3x+c

We now need to find the y-intercept, or 'c' in the equation above.

All points on this line will follow this equation. This includes the two points in the question, so we can sub in the x and y values and rearrange to find c. We can choose either of the points. Lets start with (1,-6)

x=1, y=-6

y=-3x + c

-6=-3*1 +c

-6=-3 +c

c=-3

Therefore:

y=-3x-3

We can check this by using the other coordinate:

(-2,3) 

x=-2, y=3

3=-3*-2  -3

3=6-3

3=3

As for finding the midpoint of the two points, we just need to find middle of the 2 x-coordinates and the middle of the 2 y-coordinates (need some diagrams here)

To do this, we can just find the averages.

x - coordinates: 1 and -2

x midpoint = (1+ -2)/2 = -0.5

y - coordinates: -6 and 3

y midpoint = (-6+3)/2 =-1.5

So our midpoint coordinate is (-0.5, -1.5)

Kara  V. GCSE Maths tutor, GCSE Science tutor, A Level Maths tutor, A...

2 years ago

Answered by Kara , an A Level Maths tutor with MyTutor


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

350 SUBJECT SPECIALISTS

£26 /hr

Scott R.

Degree: PGCE Secondary Mathematics (Other) - Leeds University

Subjects offered:Maths, Further Mathematics

Maths
Further Mathematics

“I am currently completing 2 PGCEs in Leeds. I have always had a passion for maths and my objective is to help as many as possible reach their full potential.”

£22 /hr

Kate P.

Degree: Mathematics (Masters) - Bath University

Subjects offered:Maths, Geography+ 1 more

Maths
Geography
-Personal Statements-

“Hi! I'm Kate. I'm a mathematics student who strives to improve students confidence, enjoyment and ability in mathematics and geography.”

Sherin W. A Level Maths tutor, GCSE Maths tutor, GCSE Further Mathema...
£20 /hr

Sherin W.

Degree: Biomedical science (Bachelors) - Sussex University

Subjects offered:Maths, Further Mathematics + 4 more

Maths
Further Mathematics
Chemistry
Biology
-Personal Statements-
-Medical School Preparation-

“For the past 5 years I have been tutoring, individuals to small classes. I am passionate about teaching and think it is an essential part of life and careers.”

MyTutor guarantee

|  2 completed tutorials

About the author

Kara V.

Currently unavailable: no new students

Degree: Evolutionary Anthropology (Masters) - Durham University

Subjects offered:Maths, Science+ 2 more

Maths
Science
Physics
Chemistry

“About me: I am currently at Durham studying for a Masters in Anthropology, after just completing my Masters in Physics at the University of York. I am looking to teach a bit of maths and science to GCSE and A level student of all abi...”

MyTutor guarantee

You may also like...

Other A Level Maths questions

Given x = 3tan(2y) find dy/dx in terms of x

Differentiate y = (3x − 2)^4

How do I integrate sin^2 (x) dx?

A curve is defined by the parametric equations x=t^2/2 +1, y=4/t -1. Find the gradient of the curve when t =2.

View A Level Maths tutors

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

mtw:mercury1:status:ok