+0  
 
0
50
1
avatar

I’ve tried so hard on this, can anyone do it?

 

The points A (6,1) and B(-2,5) are on the line with equation y=-1/2x+4 

M is the midpoint of AB

Find an equation of the line through M that is perpendicular to y=-1/2x+4

Guest Mar 18, 2018
Sort: 

1+0 Answers

 #1
avatar+92225 
+3

Hi, I can help you :)

 

The points A (6,1) and B(-2,5) are on the line with equation y=-1/2x+4 

M is the midpoint of AB

Find an equation of the line through M that is perpendicular to y=-1/2x+4

 

the gradient of the line   y=-1/2x+4   is    \( -\frac{1}{2}\)

 

The gradient of the line that is perpendicular is the negative reciprocal which is    \( +\frac{2}{1}=2\)

 

So 2 will be the gradient of the new line.

 

The midpoint of AB is simply  the average of the xes and the average of the ys     

 

\(midpoint=(\frac{6+-2}{2},\frac{1+5}{2})\\ midpoint=(\frac{4}{2},\frac{6}{2})\\ midpoint=(2,3)\\\)

So you want the equation of the line through (2,3) with a gradient of 2

there are lots of methods to do this.

Here is one, my start is a bit different from normal, I think it makes it easier because it is the same for many different questions. You just need 2 different ways to express the gradient to make it work.

 

\(\begin{align} gradient &=gradient\\ m&=\frac{y-y_1}{x-x_1}\\ 2&=\frac{y-3}{x-2}\\ 2(x-2)&=y-3\\ 2x-4&=y-3\\ 2x-1&=y\\ y&=2x-1 \end{align} \)

 

I hope all that helps :)

Melody  Mar 18, 2018

35 Online Users

avatar
avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details